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3 years ago

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

Mathematics

1 answer:

LenaWriter [7]3 years ago

8 0

Answer: 27.69⁰

Step-by-step 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

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