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Maths-

General

Easy

Question

In the figure, sides QP and RQ of a $straight triangle P R R$ are produced to points S and T respectively.
If $straight angle SPR equals 135 to the power of ring operator$ and $straight angle POT equals 110 to the power of ring operator$ , find $straight angle PRQ$ .

hint Hint:

As we know Sum of ∠RPQ and ∠RPS is 180° as they are angle on straight line .We find the value of ∠ PRQ by using that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

The correct answer is: ∠ PRQ = 65°

Step 1:-Find ∠RPQ
∠RPQ + ∠RPS = 180°(angle on straight line)
∠RPQ + 135° = 180° ( given, ∠RPS =135°)
∠RPQ = 180°-135° = 45°
Step 2:- Find ∠PRQ
We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.
∠ PRQ +∠RPQ = ∠PQT
∠ PRQ + 45°= 110° (given, ∠ PQT = 110°)
∠ PRQ = 110°- 45°
∴ ∠ PRQ = 65°

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