In figure given below L parallel to m bisectors of angle RQB and angle DRQ intersects at p Find the measure of angle RPQ
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why angle DRQ+ angle BPQ = 180
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Answer:
∠RPQ = 90
Step-by-step explanation:
∠DRQ and ∠RQB form pair of adjacent angles
⇒ ∠DRQ + ∠RQB = 180
Since, PQ and PR are angle bisectors
⇒ 2x + 2∠RQP = 180
⇒ x + ∠RQP = 90
⇒ ∠RQP = 90 - x
Now , in ΔRPQ by using angle sum property of a triangle
∠RQP + ∠RPQ + ∠PRQ = 180
⇒ 90 - x + ∠RPQ + x = 180
⇒ ∠RPQ = 90
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