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Question

What is the measure of each angle of the quadrilateral formed by the angle bisectors of a parallelogram?
  1. 180° 
  2. 90° 
  3. 60° 
  4. 100° 


Solution

The correct option is B 90° 
Given, ABCD is a parallelogram,
∠A = ∠C and ∠B = D

AE, BF, CG and DH are angle bisectors.
So, ∠DAE = ∠EAB,
∠ABF = ∠FBC,
∠BCG = ∠GCD and
∠CDH = ∠ HDA

∠A + ∠B = 180°
∠EAB + ∠ABF = 90°
∠APB = 180° - (∠EAB + ∠ABF) = 90° = ∠QPS (vertically opposite angles)

Similarily, 
∠PSR = ∠SRQ = ∠RQP = 90°
 

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