If two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°, then the ratio of these angles is
(a) 1 : 3
(b) 2 : 3
(c) 1 : 4
(d) 1 : 2

Solution:

Given, the two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°

We have to find the ratio of these angles.

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

So, (5x - 5)° + (10x + 35)° = 180°

5x - 5° + 10x + 35° = 180°

15x + 30° = 180°

15x = 180° - 30°

15x = 150°

x = 150°/15

x = 10°

Now, 5x - 5 = 5(10°) - 5° = 50° - 5° = 45°

10x + 35° = 10(10°) + 35° = 100° + 35° = 135°

Required ratio = 45° : 135°

= 5 : 15

= 1 : 3

Therefore, the required ratio is 1 : 3

✦ Try This: If two adjacent angles of a parallelogram are (x - 10)° and (5x + 15)°, then the ratio of these angles is

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 16

If two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°, then the ratio of these angles is (a) 1 : 3 (b) 2 : 3 (c) 1 : 4 (d) 1 : 2

Summary:

If two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°, then the ratio of these angles is 1 : 3.

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