Question

In the above figure, m∠P = 135° and m∠Q = (5x)°. If angles P and Q are supplementary angles, what are the value of x and the measure of angle Q?

Answer 1

`\huge\boxed{\sf m \angle Q = 45\°}`

Explanation:

Given that:

m∠P = 135°

m∠Q = (5x)°

Note:

• Supplementary angles add up to 180 degrees.

So,

135 + 5x = 180

• Subtract 135 from both sides

5x = 180 - 135

5x = 45

• Divide both sides by 5

x = 45/5

x = 9

Since,

m∠Q = (5x)°

m∠Q = [5(9)]°

m∠Q = 45°

`\rule[225]{225}{2}`