Question

pls tell the answer as soon as possible

Answer 1

Answer:

The answer will be 24°.

Step-by-step explanation:

Given;

 ∠R = 34° and ∠Q =82°

PS is the bisector of ∠QPR.

PT is perpendicular to RQ.

∠Q + ∠PTQ + ∠TPQ = 180;

82 + 90 + ∠TPQ = 180

∠TPQ = 8°

Now, ∠R + ∠PTR + ∠TPR = 180;

34 + 90 + ∠TPR = 180

∠TPR = 56° (i)

∠TPR + ∠TPQ = ∠QPR

∠QPR = 56 + 8

= 64°

Since, PS is the angle bisector.

Thus, ∠RPS = ∠QPS;

∠RPS + ∠QPS = ∠QPR

∠RPS + ∠RPS = ∠QPR

∠RPS = 64 / 2

= 32° (ii)

Therefore, ∠TPS = ∠TPR - ∠RPS; (from i & ii)

= 56° - 32°

= 24°.

That's all.