Question

The given figure shows a square ABCD and
an equilateral triangle ABP.
Calculate :
(i) angle AOB
(ii) angle BPC
(iii) angle PCD
(iv) reflex angle APC


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Answer 1

Given :   figure shows a square ABCD and  an equilateral triangle ABP.

To find : Calculate :

(i) angle AOB

(ii) angle BPC

(iii) angle PCD

(iv) reflex angle APC

Solution:

∠BOA = 60°  ( Equilateral triangle)

∠ABO = 45°  ( O lies on Diagonal and diagonal makes angle 45°)

=> ∠AOB = 180° - 60° - 45°  = 75°

∠AOB  = ∠OPB + ∠PBO

=> 75° = 60° + ∠PBO

=> ∠PBO = 15°

=> ∠CBP = 45° - 15° = 30°

BP = BC  

=> ∠BPC = ∠BCP

∠BPC + ∠BCP + ∠CBP = 180°

=> 2 ∠BPC = 150°

=> ∠BPC =  ∠BCP  = 75°

∠PCD = 90° - 75°

=> ∠PCD = 15°

∠APC = 60° + 75° = 135°

Reflex ∠APC = 360° - 135° = 225°

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