SOLUTION: A regular polygon ABCDE is inscribe in a circle, centre O, calculate 1. A angleB D 2. AOD

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Question 1130643: A regular polygon ABCDE is inscribe in a circle, centre O, calculate 1. A angleB D 2. AOD
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
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calculate

1. < A+B+D = > < A+B+O + <O+B+D
< A+B+O=360%2F5=72+

observe triangle O+B+D: -> angle BOD=144 and the < O+B+D=< ODB
so, < O+B+D=%28180-144%29%2F2=36%2F2=18
hens < A+B+D+=+72%2B18=90+

2. < AOD = <AOE+ < EOD=360%2F5%2B360%2F5=2%2A72=144



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The answer to the first question from tutor MathLover1 is wrong. She incorrectly stated that angle ABO is 72 degrees.

And in general her methods are more work than necessary to answer the questions.

The 5 arcs cut off by the sides of the regular pentagon are each 72 degrees.

Question 1: Angle ABD is an inscribed angle that cuts off an arc of 2*72 = 144 degrees; the measure of inscribed angle ABD is half the intercepted arc: 72 degrees.

Question 2: Angle AOD is a central angle that cuts of an arc of 2*72 = 144 degrees; the measure of central angle AOD is equal to the measure of the intercepted arc: 144 degrees.