Question

1. ABCDE is a regular pentagon.
DEF is a straight line.
Calculate
(a) angle AEF
(b) angle DAE​

Answer 1

Given : ABCDE is a regular pentagon . DEF is a straight line

To Find :

∠AEF

∠DAE

Solution:

Exterior angle of a regular  polygon  =   360°/n

n = number of sides of polygon

Pentagon has 5 sides

=> n = 5

Exterior angle  = 360°/5  = 72°

∠AEF is exterior angle of pentagon

=> ∠AEF = 72°

∠AEF   = ∠ADE + ∠DAE   ( exterior angle of triangle = Sum of opposite two interior angles)

∠ADE =  ∠DAE   ( ∵ DE = AE )

=>  ∠AEF   =  ∠DAE  +  ∠DAE

=>  ∠AEF   = 2 ∠DAE

∠AEF = 72°

=>  2 ∠DAE = 72°

=> ∠DAE = 36°

∠AEF = 72°

∠DAE = 36°

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