Question

Sam prepared a project for rain water harvesting. Diagrammatic representation of the project is given below.PQ and PR are two pipes touching the circular pit and meets at an angle of 60". Find QSR.​

Answer 1

Answer:

60°

Step-by-step explanation:

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Answer 2

The measure of angle QSR is 60°.

Given:

∠QPR = 60°

To Find:

∠QSR

Solution:

As PQ and PR are tangents to the circle ⇒ ∠PQO and ∠PRO will be equal to 90°

Now, as the sum of the 4 angles of a quadrilateral is equal to 360°, therefore, in quadrilateral PROQ,

∠PQO + ∠PRO + ∠QPR + ∠ROQ = 360

90 + 90 + 60 + ∠ROQ = 360

∠ROQ = 360 - 240

∠ROQ = 120°

Now, since ∠ROQ and ∠QSR are angles formed on the same chord RQ,

∠QSR = 1/2 × ∠ROQ

∠QSR = 1/2 × 120

∠QSR = 60

Thus, the measure of angle QSR is 60°.

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