Question

Find m∠Y if m∠Y is six more than three times its supplement.

Answer 1

136.5°

Explanation:

"
`m\angle Y` is six more then three times its supplement".

Three times refers to multiply by 3, and six more implies and addition.

Supplement indicates that the sum of those angles is 180°.

So, the problem can be expressed as

`m \angle Y=3(180-m\angle Y)+6`

Solving for angle Y, we have

`m \angle Y=540-3m\angle Y+6\\m \angle Y+3m \angle Y=546\\4m \angle Y=546\\m \angle Y=(546)/(4)=136.5`

And the supplement is

`180 - m\angle Y=180-136.5=43.5`

Therefore, the angle is 136.5°.

Answer 2

To answer this item, we let x be the measure of angle Y. If we say supplement, it is understood that when we sum up the measures of the two angles (angle Y and its supplement) the answer should be 180. Therefore the other angle is 180-x. Going back to the condition given in this item, we will be able to generate an equation,
x = 3(180 - x)
The value of x from the equation is 135. Thus, m∠Y is 135°.