17) In the given figure, O is the centre of circle, angle OPQ = 27° and angle ORQ = 21°then find the values of
angle
POR and angle PQR.
Answers
Given : O is the centre of circle, angle OPQ = 27° and angle ORQ = 21°
To Find : values of angle POR and angle PQR.
Solution:
OP = OQ = Radius
=> ∠OPQ = ∠OQP
=> ∠OQP = 27°
OR = OQ = Radius
=> ∠OQR = ∠ORQ
=> ∠OQR = 21°
∠PQR = ∠OQP + ∠OQR
=> ∠PQR = 27° + 21°
=> ∠PQR = 48°
∠POR = 2∠PQR
=> ∠POR = 2*48°
=> ∠POR = 96°
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Step-by-step explanation:
OP = OQ = Radius
=> ∠OPQ = ∠OQP
=> ∠OQP = 27°
OR = OQ = Radius
=> ∠OQR = ∠ORQ
=> ∠OQR = 21°
∠PQR = ∠OQP + ∠OQR
=> ∠PQR = 27° + 21°
=> ∠PQR = 48°
We know that, ∠POR = 2∠PQR
=> ∠POR = 2*48°
∴ ∠POR = 96°