Question

O is the center of a circle that passes through P,Q,R and S as shown in the figure SR is produced to X. If angle QRX= 133°, find x​

Answer 1

Given:

A figure in which O is the center of a circle that passes through P, Q, R and S. SR is produced to X. Also, angle QRX= 133° and angle SPQ = 4x + 13°

To find:

The value of x.

Solution:

The value of x is 30°.

To answer this question, we will follow the following steps:

As given, we have,

angle QRX= 133°

So,

angle QRX + angle QRS = 180°

(as the sum of all angles on one side of the straight line is equal to 180°)

133° + angle QRS = 180°

angle QRS = 180°-133°

angle QRS = 47°

Now,

PQRS is a cyclic quadrilateral in which the sum of opposite angles is equal to 180°

Angle SPQ + Angle QRS = 180°

(4x + 13)° + 47° = 180°

4x + 60° = 180°

4x = 120°

x = 30°

Hence, the value of x is 30°.

Answer 2

Step-by-step explanation:

firstly, we know that angel QRS +QRX=180°[LINEAR PAIR]