In a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
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Can you please help me out with a question
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AS shown in the figure:
The measure of arc RT = 27
The measure of arc FN = 105
The measure of angle FUN will be as follows:
[tex]m\angle\text{FUN}=\frac{1}{2}(105+27)=\frac{1}{2}\cdot132=66[/tex]So, the answer is option C. 66
Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7
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(a)
[tex]\log _59-\log _511=\log _{5_{}}(\frac{9}{11})\text{ (}\because\log a-\log b=\log (\frac{a}{b})[/tex]Thus, the required value in the blank in 9/11/
(b)
[tex]\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)[/tex]Thus, the required value in the blank is 9.
(c)
[tex]\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}[/tex]Thus, the requried value in the blank is 32.
4x + x + 4 = 8x -3x + 4
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x can take any real value
Explanation
[tex]4x+x+4=8x-3x+4[/tex]
Step 1
add similar terms in both sides
[tex]\begin{gathered} 4x+x+4=8x-3x+4 \\ 5x+4=5x+4 \end{gathered}[/tex]Step 2
subtract 5x+4 in both sides
[tex]\begin{gathered} 5x+4=5x+4 \\ 5x+4-(5x+4)=5x+4-(5x+4) \\ 0=0 \end{gathered}[/tex]0=00 means that as an equation, its solution is that x can take any real value .
I hope this helps you
A construction worker dropped a hammer while building the Grand Canyon skywalk, 8100 feetabove the Colorado River. Use the formula t=(square root of h)/4 to find how many seconds it took for thehammer to reach the river.
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Given:
[tex]t=\frac{\sqrt[]{h}}{4}[/tex]To find the time when the height h=8100 feet:
Substitute h=8100 in the given function.
[tex]\begin{gathered} t=\frac{\sqrt[]{8100}}{4} \\ t=\frac{90}{4} \\ t=22.5\text{ seconds} \end{gathered}[/tex]Thus, the time required for the hammer to reach the river is 22.5 seconds.
I need help with this practice problem solving The subject is trigonometry It asks to graph the functionIf you can, use Desmos to graph… it is recommend
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In order to determine the graph of the given function, cosider:
The function f(x) is indetermined when the argument of the cot is 0.
[tex]\begin{gathered} x+\frac{\pi}{6}=0 \\ x=-\frac{\pi}{6} \end{gathered}[/tex]In this case, the period is 2pi. Then, not only for x=-pi/6, but for x=5pi/6 the function is indeterminate.
Then, the graph is:
help meeeeeeeeeeeeeeeee
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For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
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need help with excerise step by step been 20 year's
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Given:
Standard deviation
[tex]\sigma=5.18[/tex]Mean
[tex]\mu=129[/tex]Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
which numbers are all divisible by 5
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Answer:
numbers that end with 0 or 5.
Answer: 5 35 790 55
Step-by-step explanation:
kekera pere
A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)
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a.
Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.
The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.
It can be represented by the expression C(x);
[tex]C(x)=120+30x[/tex]b.
Graphing of the function, we would have;
c.
If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;
[tex]F(x)=420+10x[/tex]graphing the above function, we have;
the first plan is represented by the blue line while the second plan is represented by the red line.
d.
The number of months after which the second plan is less expensive is the value of x when the two lines meet.
the two lines meet at point;
[tex](15,570)[/tex]The value of the x coordinate is 15.
So, The number of months after which the second plan is less expensive is
[tex]15\text{ months}[/tex]CS 18 and 105 calories in each juice box The rules for two horseback riding packages are shown below. Go Galloping Horseback Rides $6 equipment fee plus S10 per hous hours horseback riding and let yepresent the total cost of the package. Write a system of equations to represent this situation let x represent the number of Lucky Horseshoe Stables $12 equipment fee plus hour 259 Calories What is the solution to the system of equations? What does the solution represent?
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8A) Let x represent the number of hours of horseback riding.
Let y represent the total cost of the package
If Lucky horseshoe stables is used for x hours, the equation for the total cost would be
y = 7x + 12
If Go galloping horseshoe rides is used for x hours, the equation for the total cost would be
y = 10x + 6
Thus, the equations are
y = 7x + 12
y = 10x + 6
B) To solve the system of equations, we would substitute the first equation into the second equation. It becomes
7x + 12 = 10x + 6
10x - 7x = 12 - 6
3x = 6
x = 6/3
x = 2
y = 7x + 12 = 7 * 2 + 12
y = 14 + 12
y = 26
The solution of the system of equations is (2, 26)
Hugo averages 42 words per minute on a typing test with a standard deviation of 5.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(42,5.5). Suppose Hugo types 60 words per minute in a typing test on Wednesday. The z-score when x=60 is ________. This z-score tells you that x=60 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above.
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The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
Given,
Consider as a normal distribution:
The mean should be equals to 42 (μ)
The standard deviation (σ) = 5.5
We have to find the z score when x = 60.
That is,
z = (x - μ) / σ = (60 - 42) / 5.5 = 18/5.5 = 3.27
Therefore,
The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
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the jar's inner dimensions are approximately a rectangular prism with dimensions of 14cm by 12cm by 28cm. George estimates that the lowest amount of marbles possible to fill the jar 225 marbles and the highest amount is approximately 489 marbles. what is the reasonable lower limit and upper limit for the amount of marbles in the jar according to Fermi?
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Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm
Larry says all numbers that have a 2 in the one's place are composite numbers. Explain if Larry is correct or incorrect.
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A composite number is defined as a whole number that have more than two factors; from this definition we conclude that all whole numbers that are not prime are composite numbers.
Since all even numbers are not prime we conclude that Larry is correct; all numbers that have a 2 in the one's place are composite. In fact all even numbers are composite with exception of 2 itself.
What is the area in square feet ( of the rectangle) of 4 3/4 feet and 6 4/5 feet
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Recall the area of a rectangle is determined by the formula
[tex]\begin{gathered} A_{\text{rectangle}}=lw \\ \text{where} \\ l\text{ and }w\text{ are the dimensions of the rectangle} \end{gathered}[/tex]Given the following
w = 4 3/4 ft
l = 6 4/5 ft
Convert the following given into improper fraction first
[tex]\begin{gathered} w=4\frac{3}{4}\text{ ft}\Longrightarrow w=\frac{19}{4}\text{ ft} \\ l=6\frac{4}{5}\text{ ft }\Longrightarrow l=\frac{34}{5}\text{ ft} \end{gathered}[/tex]Next, substitute those values to the given formula for solving the area of the rectangle
[tex]\begin{gathered} A=lw \\ A=\frac{34}{5}\text{ ft}\cdot\frac{19}{4}\text{ft} \\ A=\frac{646}{20}\text{ ft}^2 \\ \text{Convert the final answer back into mixed fractions} \\ A=\frac{646}{20}\text{ ft}^2\Longrightarrow A=32\frac{3}{10}\text{ ft}^2 \\ \\ \text{Therefore, the area of the rectangle is} \\ 32\frac{3}{10}\text{ ft}^2 \end{gathered}[/tex]Find the value of k so that x-1 is a factor of x^2 - 2x^2 + 3x + k
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The value of k so that x - 1 is a factor of the polynomial, x² - 2x² + 3x + k is -2.
How to find the factor of a polynomial?The polynomial given is x² - 2x² + 3x + k.
Let's find the value of k so that x - 1 is a factor of the polynomial x² - 2x² + 3x + k.
Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore, the value of k that will make x - 1 a factor is when the polynomial is equals to zero when we input the root of x - 1 in the polynomial.
Hence,
x - 1 = 0
x = 1
let's substitute the value of x in the polynomial. The polynomial must be equals to 0 for x - 1 to be a factor of the polynomial.
0 = x² - 2x² + 3x + k
0 = (1)² - 2(1)² + 3(1) + k
0 = 1 - 2 + 3 + k
0 = - 1 + 3 + k
0 = 2 + k
k = - 2
Therefore, the value of k is -2.
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You have 1/5 of a box of erasers and you need to share them with 3 total people, including yourself. What fraction of the box should each person get?
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You have 1/5 of a box of erasers
Number of box of erasers = 1/5.
you need to share them with 3 total people, including yourself
Total number of people = 3 + 1( yourself)
Total number of people = 4
Since, we have to distribute the box of erasers to 4 people
So, divide 1/5 by 4:
[tex]\begin{gathered} \frac{1}{5}\text{ }\div4=\frac{\frac{1}{5}}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5}\times\frac{1}{4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{5\times4} \\ \frac{1}{5}\text{ }\div4=\frac{1}{20} \end{gathered}[/tex]The fraction of the box that each person will get is 1/20
Answer: 1/20
through: (5,-4), slope = -9/5
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The slope intersept form of a line is ,
[tex]y-y_1=m(x-x_1)[/tex]Given the point (x1,y1) is (5,-4) and slope is -9/5 implies,
[tex]undefined[/tex]How many solutions does this equation have?-4k + 4k = 0
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Let's try so solve this equation:
[tex]\begin{gathered} -4k+4k=0 \\ 0=0 \end{gathered}[/tex]When you have a result of 0 = 0, that means the equation has infinite solutions, that is, any value of k we use would satisfy the equation.
So the equation has infinitely many solutions.
I tried it and got imaginary numbers in the answer.
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Given the following equation:
[tex]\frac{x}{x-4}-\frac{4}{x}=\frac{3}{x-4}[/tex]First, we will identify the zeros of the denominator
So, the zeros are: x = {0,4}
Second, multiply the equation by x(x-4) to eliminate the denominators
[tex]x(x-4)*(\frac{x}{x-4}-\frac{4}{x})=x(x-4)*\frac{3}{x-4}[/tex]Simplify the equation:
[tex]x^2-4(x-4)=3x[/tex]Expand the equation and combine the like terms:
[tex]\begin{gathered} x^2-4x+16=3x \\ x^2-7x+16=0 \end{gathered}[/tex]The last quadratic equation will be solved using the quadratic rule:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substitute a = 1, b = -7, c = 16
[tex]\begin{gathered} x=\frac{7\pm\sqrt{(-7)^2-4(1)(16)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt{-15}}{2}=\frac{7\pm i\sqrt{15}}{2} \\ \\ x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace \end{gathered}[/tex]So, the answer will be:
[tex]x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace[/tex]4. Betty Kusack and Theresa Peña together can do a job in 20 hours. Working alone,Betty can do the job in 60 hours. How long would it take Theresa, working alone, todo the job?AnswerH
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Given:
Betty and Theresa together complete a job in 20 hours.
Betty alone does a work in 60 hours.
The aim is to find the time Theresa will take to complete the job alone.
Therefore,
Betty and Theresa's 1 day work:
[tex]=\frac{1}{20}[/tex]Betty's 1 day work when he works alone:
[tex]=\frac{1}{60}[/tex]Now, Theresa's 1 day work when he works alone is given by:
[tex]\begin{gathered} =\frac{1}{20}-\frac{1}{60} \\ =\frac{3-1}{60} \\ =\frac{2}{60} \\ =\frac{1}{30} \end{gathered}[/tex]Hence, Theresa can do the job in 30 hours working alone.
Triangle ABC is shown with exterior ∠z.
Determine m∠z.
49°
97°
131°
146°
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Answer:
(c) 131°
Step-by-step explanation:
Given exterior angle z of a triangle with remote interior angles 97° and 34°, you want the measure of angle z.
Remote interior anglesAn exterior angle is equal to the sum of the remote interior angles.
Applicationz = 97° +34°
z = 131°
Bobby was making a road trip to visit his parents. He stopped for gas and bought x number of gallons for $2.25 per gallon and a soda for $1.75. How much did he spend at the gas station if her purchased 15 gallons of gas?
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Answer:
$35.5
Explanation:
If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:
15 x $2.25 = $33.75
Adittionally, Bobby bought a soda for $1.75, so he spend a total of:
$33.75 + $1.75 = $35.5
So, he spends $35.5
Can someone please help me on this question, I'm a little stuck? The question should be down below!
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We have a right triangle with a missing side.
When we have two sides given sides on the right triangle and we need to find the missing side, we use the Pythagoras theorem:
The formula is given by:
[tex]a^2=b^2+c^2[/tex]Where:
a = Hypotenuse
b= Opposite side
c= Adjacent side
Now, we need to label the sides of the given triangle:
The largest side, represents the hypotenuse, in this case, a=15m.
The adjacent side is between the 90 degrees angle and the hypotenuse, in this case, c = 9m
Therefore, the missing side is the opposite side, let set b for this side:
Replacing these values:
[tex](15m)^2=b^2+(9m)^2[/tex][tex]225=b^2+81[/tex]Solve the equation for b:
[tex]225-81=b^2[/tex][tex]144=b^2[/tex][tex]\sqrt[]{144}=\sqrt[]{b^2}[/tex]Therefore, the missing side:
[tex]12=b[/tex]
Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−4, −1), B′(0, 1), C′(−2, −4) A′(−4, 7), B′(0, 9), C′(−2, 4) A′(0, 3), B′(4, 4), C′(3, 0) A′(−8, 7), B′(−4, 9), C′(−6, 4)
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Given:
The triangle is ABC
Vertices of ABC is
[tex]\begin{gathered} A=(-4,3) \\ \\ B=(0,5) \\ \\ C=(-2,0) \end{gathered}[/tex]Find-:
The vertex after 4 units down
Explanation-:
The triangle is down, which means changing the coordinates of the y-axis
The y axis reduce by 4 units, then coordinates is
[tex]\begin{gathered} A=(-4,3) \\ \\ A\rightarrow A^{\prime} \\ \\ A^{\prime}=(-4,(3-4)) \\ \\ A^{\prime}=(-4,-1) \end{gathered}[/tex]The B' is
[tex]\begin{gathered} B=(0,5) \\ \\ B^{\prime}=(0,(5-4)) \\ \\ B^{\prime}=(0,1) \end{gathered}[/tex]The C' is
[tex]\begin{gathered} C^{\prime}=(-2,(0-4)) \\ \\ C^{\prime}=(-2,-4) \end{gathered}[/tex]So, the new coordinates are
[tex]\begin{gathered} A^{\prime}(-4,-1) \\ \\ B^{\prime}(0,1) \\ \\ C^{\prime}(-2,-4) \end{gathered}[/tex]the line AB is drawn on the grid.(i) Write down the coordinates of A
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The coordinate of point A = (0, 1)
Explanation:Given:
the line AB is drawn on the grid
To find:
the coordinates of A
The coordinates of a point is in the form: (x, y)
To determine the coordinates of A, we will trace the y axis and x-axis.
At point A, x = 0, y = 1
The coordinate of point A = (0, 1)
The triangles below are congruent by SSS, so we can say that < E is congruent to ______ by CPCTC.
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The triangles are given to be congruent by the side-side-side (SSS) congruence property.
Hence, the congruent statement is:
[tex]\triangle DEF\cong\triangle HIJ[/tex]It is required to complete the given statement.
Recall that CPCTC means Corresponding Parts of Congruent Triangles are Congruent.
The corresponding part to ∠ E is ∠I. Hence, by CPCTC, the angle congruent to ∠E is ∠I.
The answer is option b.
lan is working two summer jobs, making $19 per hour lifeguarding and making $9per hour clearing tables. In a given week, he can work no more than 14 total hoursand must earn a minimum of $180. If x represents the number of hours lifeguardingand y represents the number of hours clearing tables, write and solve a system ofinequalities graphically and determine one possible solution.Inequality 1: y 24plot switch shadeInequality 2: y 24plotswitch shade2019181716151413121110Yes
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Given:
Lan is working two jobs:
1) $19 per hour life guarding
2) $9 per hour clearing tables
The total hours per week = 14
He must earn a minimum of $180
Let x represents the number of hours life guarding and y represents the number of hours clearing tables
So, we have the following inequalities
[tex]\begin{gathered} x+y\le14 \\ 19x+9y\ge180 \end{gathered}[/tex]We need to solve the inequalities by graph
So, we will graph the lines: x + y = 14 and 19x + 9y = 180
The shaded area represents the solution of the system of inequalities
The following figure represents the solution of the system of inequalities
uhh im stuck and im stressed .. and i dont understand area model math..
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(5x + 6)(2x² + 3x + 8) = ?
Step 02:
Area Model
First, you must multiply the values in the rows by each of the values in the columns.
Then, you must add all the values resulting from the multiplications.
10x³
2x²
+ 12x²
15x²
18x
3x
40x
48
8
--------------------------------------------
10x³ + 29x² + 61x + 56
The answer is:
(5x + 6)(2x² + 3x + 8) = 10x³ + 29x² + 61x + 56
Three different transformation are performed on the shaded triangle. Each transformation results in on of three images. Match each image to the transformation applied on the shaded triangle
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We are given a triangle and three possible transformations performed on it. The first transformation shows that the triangle has no change in orientation, therefore, this transformation is a translation only.
For image 2 we notice that the orientation of the triangle changes. If we draw a horizontal line in the middle of the shaded triangle and image 2 we notice that these two images are related by a reflection, also after this reflection the image was translated therefore, for image two we have reflection across a horizontal line followed by a translation.
For image 3 we can draw a vertical line in the middle of the shaded triangle and image 3 and we do a reflection across this vertical line since there is a change in the orientation of the figure.
A road sign is in the shape of a regular pentagon. What is the measure of each angle on the sign? Round to the nearest tenth. 540 252 54 Od 108
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Internal angles of a polygon
The triangle has n=3 sides, and the sum of its internal angles is 180°
The rectangle has n=4 sides, and the sumo of its internal angles is 360°
There is a general formula to calculate the sum of the internal angles of any polygon of n sides:
Sum = 180° ( n -2 )
For a pentagon (n=5), the sum of angles is:
Sum = 180° ( 5 -2 ) = 180° * 3 = 540°
We are required to find the measure of each internal angle. Since the pentagon is regular, all of its internal angles measure the same, thus:
The measure of each angle = 540° / 5 = 108°