Question

the interior angle of a n-sided polygon exceeds its interior angle by 135...find the value of n

Answer 1

Answer:

ans

Step-by-step explanation:

n= no. of sides

The sum of the interior angles =180(n−2)

The interior angle in the question , x, exceeds or is bigger than the extrerior angle by 135

Interior angle =x

Exterior angle =x−135

As the sum of the interior angle and exterior angle is 180°, we know that x+x−135=180

2x−135=180

2x=315

x=144°. This is the interior angle therefore the exterior angle is 144−108=36.

Interior angle =144°

Exterior angle =36°

As the number of interior angles is the same as the number of sides, if we multiply n by 144 we get the sum of the interior angles and we can equate that to the formula: 180(n−2).

144n=180(n−2)

144n=180n−360

−36n=−360

n=10. This particular polygon has 10 sides.