Question

show that an interior angle of a regular pentagon is 3times an exterior angle of a regular decagon​

Answer 1

Answer:

One interior angle of Pentagon = ( n - 2 ) × 180 / n

Here n = no. of sides of polygon.

In Pentagon no. of sides is 5.

So , ( 5 - 2 ) × 180 / 5

=》 3 × 180 / 5

=》 3 × 36

=》 108°

Exterior angle of any polygon is 360°.

So , Exterior angle of decagon = 360°

In decagon no. of sides = 10

One Exterior angle of decagon = 360 / n

= 360 / 10

= 36°

ATQ , we have show that an interior angle of pentagon is 3 times an exterior angle of decagon.

So , One interior angle of Pentagon = 3 times an Exterior angle of decagon

=》 108 = 3 × 36

=》108 = 108

Therefore, it's proved that one interior angle of pentagon is equal to 3 times an Exterior angle of decagon.

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