In a parallelogram PQRS, if ∠P = 60°, then other three angles are
(a) 45°, 135°, 120°
(b) 60°, 120°, 120°
(c) 60°, 135°, 135°
(d) 45°, 135°, 135°

Solution:

Given, PQRS is a parallelogram

The measure of ∠P is 60°.

We have to find the measure of the other three angles.

We know that the sum of adjacent angles in a parallelogram are supplementary.

So, ∠P + ∠Q = 180°

60° + ∠Q = 180°

∠Q = 180° - 60°

∠Q = 120°

We know that the opposite angles in a parallelogram are equal.

So, ∠P = ∠R

Now, ∠R = 60°

Similarly, ∠S = ∠Q

Now, ∠S = 120°

Therefore, the other three angles are 120°, 60° and 120°.

✦ Try This: In a parallelogram ABCD, if ∠A = 50°, then other three angles are

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 30

In a parallelogram PQRS, if ∠P = 60°, then other three angles are (a) 45°, 135°, 120° (b) 60°, 120°, 120° (c) 60°, 135°, 135° (d) 45°, 135°, 135°

Summary:

In a parallelogram PQRS, if ∠P = 60°, then other three angles are 120°, 60°, 120°.

☛ Related Questions:

• If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are (a) . . . .
• If PQRS is a parallelogram, then ∠P - ∠R is equal to (a) 60° (b) 90° (c) 80° (d) 0°
• The sum of adjacent angles of a parallelogram is (a) 180° (b) 120° (c) 360° (d) 90°