SOLUTION: ABCDE is a regular pentagon. Find the angles of triangle ADC.

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Question 1162398: ABCDE is a regular pentagon. Find the angles of triangle ADC.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The sum of the interior angles of an n-sided polygon is

SUM = (n-2)∙180°

So for a pentagon, the sum is

SUM = (5-2)∙180° = 3∙180° = 540°

Since all interior angles of a regular pentagon are equal, we
divide that by 5, and get 540°÷5 = 108°

So each of the interior angles of the pentagon measures 108°.

Since ∠B = 108° and ΔABC is isosceles, its base angles are 36° each, and the
same for ΔAED.  

Since all three angles at A add to 108°, ∠DAC also = 36°.

Since ΔADC is isosceles, its base angles are equal and 72° each.

Now you have all the angles of ΔADC.




Edwin
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