Question

PQRS IS A CYCLIC QUADRILATERAL.IF ANGLE QRS=110,FIND ANGLE SPQ

Answer 1

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Answer 2

Given:

PQRS is a cyclic quadrilateral

Angle QRS=110°

To find:

Angle SPQ

Solution:

The measure of angle SPQ is 70°.

We can find the angle by following the given steps-

We know that PQRS is a cyclic quadrilateral.

In a cyclic quadrilateral, the angles opposite to each other are supplementary.

So, the sum of opposite angles of a cyclic quadrilateral is 180°.

In PQRS, angle QRS=110°. (Given)

The angle opposite to angle QRS is the angle SPQ.

The sum of angle SPQ and angle QRS will be equal to 180°.

Angle SPQ+ Angle QRS=180°

On putting the values, we get

Angle SPQ+ 110°=180°

Angle SPQ=180°-110°

Angle SPQ=70°

Therefore, the measure of angle SPQ is 70°.