Question

The exterior angles of octagon are.2x.234x3,6x7x and 8 What is the measure of the smallest interior angle of this octagon​

Answer 1

The smallest interior angle of this octagon is 100°

Explanation:

Sum of all exterior angles of a polygon = 360°

Given: The exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°,8x°.

Then, x°+2x°+3x°+4x°+5x°+6x°+7x°+8x° =360°

⇒ 36x = 360

⇒ x= 10

Since,   interior angle+  exterior angle = 180°

The smallest interior angle has the largest exterior angle.

Largest exterior angle = 8x = 8(10)°= 80°

Smallest interior angle = 180°-8°=100°

Hence, the smallest interior angle of this octagon is 100° .

Hope it helps you