Question

The interior angle sum of a convex polygon is 1,980°.

How many sides does the polygon have? If it is a regular
polygon, what is the measure of each angle? Round to
the nearest tenth, if needed.

Answer 1

Hey, just adding on to the answer below. Not sure if this is correct for everyone, but it was for me.

Answer:

Sides: 13 sides

Measure of each angle: 152.3

Explanation:

Since we know the sum of the measures of the interior angles of a convex polygon to be 1,980, we can use the angle-sum theorem formula:

(n-2)180=?

to get our answer.

Equation:

(13-2)180 = 1,980

From here we continue using the angle sum theorem but instead with the intent of finding the measure of each individual interior angle (They will all be equal to the same degree)

Use formula

(n-2)180

n

Equation:

(13-2)180

13

This will give you the answer 152.3.

Sorry if this doesn't explain everything correctly or enough, but I hope I helped. :D

(Btw, if you want more of an explanation as how to properly use formulas to get the number of sides, you can go and check out the answer before mine! It really helps, this answer was mainly to just explain the second answer the way I did it that gave me the correct answer!)

Answer 2

Answer: 27.69⁰

Explanation:

Formula for finding the internal angle of a regular polygon is

( 2n - 4 )right angle triangle or

( 2n - 4 )90°, it can also be broken down by factorizing the expression since 2 is common,

( n - 2 )180 or supplementary

Now to find the value of n which correspond to the number of sides the polygon has, we equate the formula to the angle sum of the polygon.

( n - 2 ) × 180° = 1980°

open the bracket

180n° - 360° = 1980°

180n° = 1980° + 360°

= 2340

To find n, divide by 180 which is the coefficient of n

n = ²³⁴⁰/₁₈₀

= 13

The polygon has 13, sides

To find the measure of each angle,

Recall, the sum total of external angle = 360⁰

Therefore, to find the value of each of the angles, we divide 360 by n which is 13

³⁶⁰/n

= ³⁶⁰/₁₃

= 27.69⁰