Question

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

(a) 41°

(b) 23°

(c) 67°

(d) 18°

Answer 1

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 and. This is shown in fig (2).

So we see that,

$$\begin{gathered} \angle QPS=\angle QPR+\angle RPS \\ =67°+72° \\ =139° \end{gathered}$$

(a) 41°

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

Hence the correct answer is option (a).