MCQ

*PQRS *is a cyclic quadrilateral such that *PR* is a diameter of the circle. If ∠*QPR* = 67° and ∠*SPR* = 72°, then ∠*QRS* =

#### Options

41°

23°

67°

18°

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#### Solution

Here we have a cyclic quadrilateral *PQRS* with *PR* being a diameter of the circle. Let the centre of this circle be ‘*O*’.

We are given that `angleQPR` and `angleSPR = 72°` . This is shown in fig (2).

So we see that,

\[\angle QPS = \angle QPR + \angle RPS\]

\[ = 67°+ 72° \]

\[ = 139°\]

In a cyclic quadrilateral it is known that the opposite angles are supplementary.

`angleQPS + angleQRS = 180°`

`angleQRS = 180° - angleQPS`

`= 180° - 139°`

= 41°

Concept: Cyclic Quadrilateral

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