Question

In the given figure find the measure of < RPQ

Answer 1

the measure of angle RPQ is the sum of angle 2 and angle 4

Answer 2

CD || AB
=> <RQB + <DRQ = 180 (Co-interior angles)
=> (<RQB + <DRQ)/2 = 180/2
=> <RQB/2 + <DRQ/2 = 90
=> <PQR + <PRQ = 90 -----------(1)

Now,
In Triangle PQR
<PQR + < PRQ + < RPQ = 180
=> 90 + < RPQ = 180 (using equation 1)
=> <RPQ = 90 DEGREE

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