Question

The sum of the exterior angles and the interior angles of a regular polygon is 2340 . Find the sum of interior angles , number of sides , measure of an interior angles and measure of exterior angles.


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Answer 1

Answer:

1980, 13, 142.3°, 27.7°

Answer 2

Answer:

Sum of interior angles = 1980

No. of sides = 13

The measure of an interior angle = 152.31

The measure of an exterior angle = 27.69

Step-by-step explanation:

Given,

The sum of the exterior angles and interior angles of a regular polygon is 2340

We know,

Sum of interior angles of a regular polygon = (n-2) *180, where  'n' is the number of sides of the polygon

Sum of exterior angles of a regular polygon =  360

So we have,

(n-2) *180 + 360 = 2340

n*180 - 360 +360 = 2340

n*180 = 2340

n = 2340/180

n = 13

Hence, no. of sides of the polygon = 13

Sum of interior angles = (n-2) * 180 = (13-2) *180 = 1980

Measure of an interior angle = $\frac{sum of interior angles }{no. of sides} = \frac{1980}{13}$ = 152.31

Measure of an exterior angle = $\frac{sum of exterior angles }{no. of sides} = \frac{360}{13}$  = 27.69

Hence,

Sum of interior angles = 1980

No. of sides = 13

Measure of an interior angle = 152.31

Measure of an exterior angle = 27.69