Question

An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?​

Answer 1

Given : An equilateral triangle BPC is drawn inside a square ABCD.

To Find :  Value of angle APD in degrees

Solution:

All Sides of Square are equal  and all angles are equal to 90°

All Sides of a equilateral triangle are equal  and all angles are equal to 60°

Angles opposites to equal sides of triangle  are equal

Sum of angles of  a triangle is 180°

ABCD is square  , APD is Equilateral triangle

AB = BC = CD = AD = BP = CP

∠ABC = 90°  ,  ∠CBP  =  60°

∠ABC = ∠ABP  + ∠CBP

Hence ∠ABP   = 30°

∠BAP = ∠BPA  as AB = BP

∠BAP + ∠BPA  + ∠ABP  = 180°

Hence ∠BAP = ∠BPA = 75°

Similarly ∠CPD = 75°

∠BPC = 60°

Sum of all angles at a point is 360°

Hence ∠APD = 150°

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