Question

In the given figure, PQ = PS. The value of x is​

Answer 1

Answer:

Let's take ∆ SQP

Here an exterior angle is produced

using the property,the sum of the exterior angle formed in a ∆= sum of 2 interior opposite angles

exterior angle=110°

So,PSQ+QPS=110°

So,

PSQ+PQS+QPS=180°(sum of all interior angles of a triangle are supplementary)

PSQ & QPS makes 110° in 180°

The rest is 70°

So,PQS=70°

We know PQ=PS

so,PQS=PSQ(if two opposite sides of a triangle are equal then their opposite angles are also equal)

So,PSQ=70°

PSQ+PQS+QPS=180°

70+70+QPS=180

QPS=180-140=40°

now Let's check ∆PSR

here,PRS=25°

SPR=x

PSR=?

We can See PSR+PSQ=180°(Linear Pair)

PSR+70=180

PSR=180-70=110°

So now in ∆PSR

PSR+PRS+SPR=180°(sum of all interior angles of a triangle are supplementary)

110°+25°+x=180

135+x=180

x=180-135=45

therefore,x=45°

hope it helps

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