Question

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

What is the measure of arc PQR?
190
265
275
340

Answer 1

Hello,

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

Answer A

Answer 2

Option A is correct.

The measure of Arc PQR is 190 degree

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.