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Pqrs is a Cyclic Quadrilateral Such that Pr is a Diameter of the Circle. If ∠Qpr = 67° and ∠Spr = 72°, Then ∠Qrs = - Mathematics

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°

 

 

 
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Q 16 | Page 111
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