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Question
What is the measure of each angle of the quadrilateral formed by the angle bisectors of a parallelogram?
What is the measure of each angle of the quadrilateral formed by the angle bisectors of a parallelogram?
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Solution
The correct option is C 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°
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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