Question

in the given figure , ray QS bisects angle PQR. T is a point in the interior of angle PQS. prove that angle TQS=1/2(m angle TQR-m angle PQT)

Answer 1

easy question ,easy solution

Answer 2

PLEASE REFER TO THE PICTURE FOR THE FIGURE.

ANSWER

∠TQS = 1/2 (∠PQT - ∠TQR)

∠TQS = 1/2 (∠PQT - ∠TQR) Hence, Proved

GIVEN

Ray QS bisects ∠PQR. T is a point in the interior of ∠PQS.

TO PROVE

∠TQS = 1/2(∠TQR - ∠PQT)

SOLUTION

We can simply solve the above problem as follows;

It is given,

Ray QS is the angle bisector of ∠PQR

This means that,

∠PQS = ∠SQR

Therefore,

∠PQR = 2∠PQS

We can also write it as;

∠PQR/2 = ∠PQS (Equation 1)

Now,

∠PQS = ∠PQT + ∠TQS

Putting the value of ∠PQS in equation 1

∠PQR/2 = ∠PQT + ∠TQS

∠SQR = ∠PQT + ∠TQS (Equation 2)

We know that,

∠SQR = ∠TQR - ∠TQS

Putting the value of ∠SQR in Equation 2

∠TQR - ∠TQS = ∠PQT + ∠TQS

Rearranging the angles;

∠PQT - ∠TQR = 2∠TQS

∠TQS = 1/2 (∠PQT - ∠TQR)

∠TQS = 1/2 (∠PQT - ∠TQR) Hence, Proved

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