Question

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Answer 1

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Answer 2

Answer:

No answer. Just see the solution.

Step-by-step explanation:

Considering the line ST, Line Segment PQ stands on line ST. Thus,

∠PQS + ∠PQT = 180°

∠PQT is the same angle as ∠PQR. So, we can write that ∠PQS + ∠PQR = 180°.

Similarly, ∠PRQ + ∠PRT = 180°.

But, it is given that ∠PQR = ∠PRQ.

So, ∠PQS + ∠PQR = 180° and also, ∠PRQ + ∠PRT = 180°.

Here, the second equation can be written as ∠PQR + ∠PRT = 180°.

Now, again, ∠PQS + ∠PQR = 180° and also, ∠PQR + ∠PRT = 180°. So, we can write that

∠PQS + ∠PQR = ∠PQR + ∠PRT = 180°

Or, ∠PQS + ∠PQR = ∠PQR + ∠PRT

Now, subtracting ∠PQR from LHS and RHS,

∠PQS + ∠PQR - ∠PQR = ∠PQR + ∠PRT - ∠PQR

Or, ∠PQS = ∠PRT.

That is what we have to prove. Hence proved.