Answered

if a represents the measure of an interior angle of a regular octagon and b represents the measure of an interior angle of a regular pentagon, what is the ratio a:b?

Answer :

The ratio of a : b is 5 : 4.  

Given that:-

Measure of an interior angle of a regular octagon = a

Measure of an interior angle of a regular pentagon = b

We know that sum of all the angles of a regular polygon of n sides is (n - 2)*180.

Hence, sum of all the angles of regular octagon = (8 - 2)*180 = 6*180 = 1080 degrees.

Hence, sum of all the angles of regular pentagon = (5 - 2)*180 = 3*180 = 540 degrees.

Hence, one interior angle of a regular octagon, a  = 1080/8 = 135 degrees.

Hence, sum of all the angles of regular pentagon, b = 540/5 = 108 degrees.

Hence, the ratio of a : b = 135/108 = 5 : 4.  

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https://brainly.com/question/13419413

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