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tino4ka555 [31]
3 years ago
14

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

Mathematics
1 answer:
Elena L [17]3 years ago
4 0

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.

m\angle SPQ+m\angle QRS=180^\circ

81^\circ+m\angle QRS=180^\circ

m\angle QRS=180^\circ-81^\circ

m\angle QRS=99^\circ

Now, SRT  is a straight line.

m\angle QRT+m\angle QRS=180^\circ             (Linear pair)

m\angle QRT+99^\circ=180^\circ

m\angle QRT=180^\circ-99^\circ

m\angle QRT=81^\circ               ...(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

m\angle PQR=m\angle QRT+m\angle QTR

x=81^\circ+22^\circ

x=103^\circ

Therefore, the value of x is 103 degrees.

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