Question

the exterior angles of an octagon are x°2x°,3x°,4x°,5x°,6x°,7x°,8x°. what is this size of smallest interior angle of this octagon

Answer 1

Answer:

2x

Step-by-step explanation:

the answers will be 2x

Answer 2

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° .

# Learn more :

Show that an exterior angle of a regular convex octagon is one third of its interior angle

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