Question

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

A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 70 degrees.

What is the measure of arc PQR?

110°
140°
70°
220°

Answer 1

The correct option is 4. The measure of arc PQR is 220°.

Explanation:

Given information: PQRS is a quadrilateral and the measure of angle PQR is 70 degrees.

According to the central angle theorem, that the angle inscribed on the circle is always half the measure of the central angle.

Using central angle theorem,

`\angle POR=2* \angle PQR`

`\angle POR=2* 70`

`\angle POR=140`

The measure of of arc PQR is

`Are(PQR)=360-140=220^(\circ)`

Therefore the measure of arc PQR is 220°. Option 4 is correct.