Maths-

General

Easy

Question

# In the figure, sides QP and RQ of a are produced to points S and T respectively.

If and, find.

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°

Step 2:- Find ∠PRQ

We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

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