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Asked by Topperlearning User 16th August 2017, 12:46 PM
Answered by Expert
Answer:

begin mathsize 12px style ABCDE space is space straight a space regular space pentagon
AB equals BC equals CD equals DE equals AE space and space angle straight A space equals angle ABC equals angle straight C space equals space angle CDE equals angle DEA equals 108 degree
AB equals AE
angle 1 equals angle 2 space space space space space left parenthesis agles space opposite space to space equal space sides space in space straight a space triangle space are space equal right parenthesis
In space increment ABE comma
angle straight A plus angle 1 plus angle 2 equals 180 degree
rightwards double arrow 108 degree plus 2 angle 1 equals 180 degree
rightwards double arrow angle 1 equals 36 degree rightwards double arrow angle AEB equals 36 degree
angle 3 plus angle 1 equals 36 degree space space space space space space space space space space space space space space space space space space space space space space space left parenthesis alternate space interior space angles space as space AE space parallel to BD right parenthesis
angle AED equals angle 1 plus angle 4 equals 108 degree
rightwards double arrow angle 4 equals 108 degree minus 36 degree equals 72 degree
angle BDE equals 180 degree minus open parentheses angle 3 plus angle 4 close parentheses
space space space space space space space space space space space space space equals 180 degree minus open parentheses 36 degree plus 72 degree close parentheses
space space space space space space space space space space space space space equals 72 degree end style

Answered by Expert 16th August 2017, 2:46 PM
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