Question

A quadrilateral PQRS is inscribed in a circle, as shown below

Answer 1

Answer:

Option A is correct.

The measure of Arc PQR is 190 degree

Step-by-step explanation:

Given a cyclic quadrilateral PQRS is inscribed in a circle as shown in figure.

Given: $\angle PQR = 85^{\circ}$

An intercepted arc measures twice the intercepted angle.

The intercepted angle in the given figure is Arc PQR =$2 \cdot \angle PSR$                    ......[1]

First find the $\angle PSR$;

A quadrilateral is cyclic if and only if opposite angles sum to 180°.

then;

$\angle PQR+\angle PSR =180^{\circ}$

Substitute the value of $\angle PQR = 85^{\circ}$ in above equation we get;

$85^{\circ}+\angle PSR =180^{\circ}$

Simplify:

$\angle PSR =180^{\circ}-85^{\circ} =95^{\circ}$

Now; to find the measure of arc PQR ;

[1] ⇒ Arc PQR =$2 \cdot \angle PSR$ = $2 \cdot 95 =190^{\circ}$

Therefore, the measure of arc PQR is 190 degree.

Answer 2

Hello,

mes Angle PSR= 180°-85°=95°
mes Arc PQR= 2* 95°=190°

Answer A