Question

The figure shown is a regular pentagon. What is the value of p?

a regular pentagon with one exterior angle labeled three p.

twenty-four degrees
fifty-two degrees
seventy-two degrees
one hundred eight degrees

Answer 1

@mathstudent55

Answer 2

https://gbwebacademy.brainhoney.com/Resource/16627269,7C5,0,3,0/Assets/flvs/math3_v10_gs-xml/res0101/10_01c_32_037.jpg

Answer 3

If you have a regular pentagon, that means you have 5 sides.

Answer 4

Also, all sides are congruent, and all angles are congruent.

Answer 5

I still don't know :'(

Answer 6

Using the formula of the sum of the measures of the interior angles, can you find the sum of the measures of the interior angles?

180(n - 2)

Using 5 for n.

Answer 7

so 540! :)

Answer 8

but thats not an option _-_

Answer 9

You need to learn patience. A problem like this does not consist of one single step.
We need a few steps to find the answer.
Great. All interior angles add up to 540 degrees. Correct.
Since there are 5 of them how much does each one measure?
540/5 = ?

Answer 10

I know, sorry. 540/5=108 so now that is the answer, thank you!

Answer 11

No it isn't.

Answer 12

but why not?

Answer 13

We found that each interior angle measures 108 degrees. The question is what is p, isn't it?

Answer 14

yes, yet again you are right, I am wrong, sorry.

Answer 15

Now we see that the interior angle of 108 degrees and the exterior angle measuring 3p are supplementary angles. That means their measures add up to 180 degrees.

Answer 16

so now the question is asking 3 times p + 108 = 180 correct?

Answer 17

Now we write an equation to express that and we solve it for p.

108 + 3p = 180

Subtract 108 from both sides.
Then divide both sides by 3.
Then you'll have p.

Answer 18

Correct. You got the right equation. Now solve for p.

Answer 19

so 24, correct?

Answer 20

Correct.

Answer 21

Here's another way of doing it.
The sum of the measures of the exterior angles of a polygon, taken one per vertex, is 360.
You know you have a pentagon, so you have 5 vertices. Since the pentagon is regular, all sides are congruent, all interior angles are congruent, and all exterior angles are congruent.
Since you have 5 exterior angles (one per vertex), divide 360 by 5 to find that each exterior angle measures 72 degrees.
The problem is showing that 3p = 72.
Solve 3p = 72 for p and get p = 24.