Question

If two adjacent angles of a parallelogram are
(5x – 5)°and (10x + 35)', then find the ratio of the two angles. (answer in simplest form)​

Answer 1

Answer:

1:3

Step-by-step explanation:

sum of adjacent angles is always 180

5x-5+10x+35=180

15x+30=180

15x=150

x=10

angles = 5x-5, 10x+35

======》 5*10-5, 10*10+35

======》45,135

ratio = 45/135

=====》1:3

Answer 2

Given:

The measure of two adjacent angles of a parallelogram is (5x – 5)°and (10x + 35)°.

To Find:

The ratio of the measure of the two angles.

Solution:

The given problem can be solved using the concepts of the parallelogram.

1. The measure of the two angles is given as (5x – 5)°and (10x + 35)°.

2. According to the properties of the parallelogram, the sum of the adjacent sides of the parallelogram is 180°.

=> The sum of the angles mentioned is equal to 180°,

=> (5x – 5)° + (10x + 35)° = 180°,

=> 5x + 10x - 5 + 35 = 180,

=> 15x + 30 = 180,

=> 15x = 180 - 30,

=> 15x = 150,

=> x = 150/15,

=> x = 10°.

3. The measure of two angles are,

=> 5x - 5 = 5 x 10 - 5 =  45°.

=> 10x + 35 = 10 x 10 + 35 = 135°.

=> The ratio of two angles is 45° : 135° = 1:3.

Therefore, the ratio of the two adjacent angles of the parallelogram is 1:3.