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Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are
(a) 30°, 150°, 30°, 150°
(b) 85°, 95°, 85°, 95°
(c) 45°, 135°, 45°, 135°
(d) 30°, 180°, 30°, 180°

Solution:

Given, two adjacent angles of a parallelogram are in the ratio 1 : 5

We have to find the measure of the angles.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

Let the angles be x and 5x.

From the properties of a parallelogram, the consecutive angles are supplementary.

So, x + 5x = 180°

6x = 180°

x = 180°/6

x = 30°

Now, 5x = 5(30°) = 150°

The adjacent angles are 30° and 150°.

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

Therefore, the angles of the parallelogram are 30°, 150°, 30°, 150°.

✦ Try This: Two adjacent angles of a parallelogram are in the ratio 3 : 5. Then all the angles of the parallelogram are

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 45

Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are (a) 30°, 150°, 30°, 150° (b) 85°, 95°, 85°, 95° (c) 45°, 135°, 45°, 135° (d) 30°, 180°, 30°, 180°

Summary:

Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are 30°, 150°, 30°, 150°.

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