Question

ABCD IS A RHOMBUS WITH ANGLE D=72°.PAB IS AN EQUILATERAL TRIANGLE.FIND VALUES OF X AND Y
PLEASE CAN ANYONE HELP.ME​

Answer 1

Given : ABCD IS A RHOMBUS WITH ANGLE D=72°

PAB is an equilateral triangle

To Find : Values of X and Y

Solution:

PAB Equilateral Triangle

=> AB = AP = BP

ABCD is a rhombus ,

AB = BC = CD = AD

=> AB = BC = CD = AD =  AP = BP

Rhombus is a parallelogram

Hence opposite angles are equal

=> ∠B = ∠D = 72°

=> ∠ABC = 72°

∠ABP = 60°   ( ∵ PAB Equilateral  Triangle)

∠CBP = ∠ABP + ∠ABC

=> ∠CBP = 60° + 72°

=> ∠CBP = 132°

in ΔPBC

BP = BC

=> ∠BPC = ∠BCP = x

∠BPC +  ∠BCP + ∠CBP = 180°

=> 2x +  132° = 180°

=> 2x = 48°

=> x = 24°

y = ∠APC = ∠APB -   ∠BPC

=> y = 60° - 24°

=> y = 36°

x = 24°

y = 36°

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