If APB and CQD are two parallel lines, then bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD forms

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

a square

rhombus

a rectangle

any other parallelogram

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let us first draw a diagram by using information given that APB and CQD are two parallel lines and there are angle bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD.
seo

Given, APB and CQD are two parallel lines. Let us assume that the bisectors of ∠APQ and ∠CQP meet at point M. Similarly, bisectors of ∠BPQ and ∠DQP meet at point N.
We join PM, QM, QN, PN, it forms a quadrilateral.
Now, as given APB ∥ CQD
So, alternate interiors angles will be equal ∠APQ = ∠PQD
Now, as PM and QN are angle bisectors of ∠APQ and ∠PQD respectively. So,
∠APM = ∠MPQ and ∠BPN = ∠NPQ
∠MPQ = ∠NQP
As these are alternate interior angles so the lines PM and QN must be parallel.
Similarly, alternate interiors angles ∠BPQ = ∠CQP are also equal.
So, the lines PN and QM must be parallel.
As PM ∥ QN and PN ∥ QM.
Opposite sides are parallel to each other, it means PMQN is a parallelogram.
As CQD is a straight line, so the measure of ∠CQD = 180