Question

PQRS एक चक्रीय चतुर्भुज है। यदि ∆Q = 65° तथा
∆R = 65° हो, तो ∆P और ∆S ज्ञात कीजिए।
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Answer 1

Given:

PQRS is a cyclic quadrilateral

∠Q = 65°

∠R = 65°

To find:

∠P and ∠S

Solution:

According to the properties of a cyclic quadrilateral, we can say

The sum of either pair of opposite facing angles of a cyclic quadrilateral is 180°.

So,

∠Q + ∠S = 180°

substituting ∠Q = 65°, we get

⇒ 65° + ∠S = 180°

⇒ ∠S = 180° - 65°

⇒ ∠S = 115°

Similarly, we have

∠P + ∠R = 180°

substituting ∠R = 65°, we get

⇒ ∠P + 65° = 180°

⇒ ∠P = 180° - 65°

⇒ ∠P = 115°

Let's verify:

∠P + ∠Q + ∠R + ∠S

substituting values of the angle P, Q, R & S, we get

= 115° + 65° + 65° + 115°  

= 360°  ..... [satisfies the angles sum property of a quadrilateral]

Thus,

$\boxed{\bold{\angle P = \underline {115\°}}}\\\\\boxed{\bold{\angle S = \underline {115\°}}}$

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