In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.​

Given:

PQRS is a circle, PQT and SRT  are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

Now, SRT  is a straight line.

            (Linear pair)

              ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

Therefore, the value of x is 103 degrees.

250

step-by-step explanation: