Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th
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In the given figure, ∠POQ = 100° and ∠PQR° = 30°, then find ∠RPO - Mathematics

Sum

In the given figure, ∠POQ = 100° and ∠PQR° = 30°, then find ∠RPO

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Solution

∠PRQ = `1/2 ∠"POQ"` ...(Angles at the circumference)

= `1/2 xx 100^circ`

= 50°

∠OPQ + ∠OQP = 180° – 100° ...(Total angles of A is 180°)

= 80°

∴ ∠OPQ = `80/2`

= 40°  ...(Since OP = OQ, radius of the circle)

∠RPQ = 180° − (30 + 50)°

= 100°

∴ ∠RPO = ∠RPQ – ∠OPQ

= 100° – 40°

= 60°

Concept: Theorem: If One Side of a Cyclic Quadrilateral is Produced Then the Exterior Angle is Equal to the Interior Opposite Angle.
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APPEARS IN

Samacheer Kalvi Mathematics Class 9th Tamil Nadu State Board
Chapter 4 Geometry
Exercise 4.4 | Q 9 | Page 174
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