Mathematics
In the adjoining figure, O is the centre of the circle. If QR = OP and ∠ORP = 20°, find the value of 'x' giving reasons.
Circles
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Answer
Given,
QR = OP ⇒ QR = OQ
⇒ ∠QOR = ∠ORQ = 20° (∵ angles opposite equal sides of a triangle are equal)
Exterior angle in a triangle is equal to the sum of two opposite interior angles.
∴ ∠OQP = ∠QOR + ∠ORQ = 20° + 20° = 40°.
As OP = OQ, ∠OPQ = ∠OQP
⇒ ∠OPQ = 40°
⇒ ∠OPR = 40°.
Exterior angle in a triangle is equal to the sum of two opposite interior angles.
∴ x = ∠TOP = ∠OPR + ∠ORP = 40° + 20° = 60°.
Hence, the value of x = 60°.
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