Question

The measure of a supplement of an angle is 36 more than three times the measure of the angle. Find the measures of the angle and its supplement.

a) 30 ∘ and 150∘

b) 40∘and 120∘

c) 45 ∘ and 135∘

d) 50∘ and 110∘

Answer 1

The measures of the angle and its supplement is b) 40∘ and 120∘.

Step-by-step explanation:

The measure of an angle and its supplement adds up to 180∘ because they are supplementary angles. Let's denote the measure of the angle as
`x`. The supplement of the angle is then
`180 - x.`

According to the given information, the supplement is 36 more than three times the measure of the angle:

`180 - x = 3x + 36`

Solving for
`x:`

`4x = 144`

`x = 36`

So, the measure of the angle is 36∘, and its supplement is:

180 - 36 = 144∘

In summary, the correct answer is b) 40∘ and 120∘.