Question

The supplement of an angle is six and a half times as large as the complement of the angle. What is the measure of the supplement angle to the nearest hundredth of a degree?

A) 101.25°

B) 104.22°

C) 106.36°

D) 108.63°

Answer 1

C) 106.36

Explanation:

Let x be the given angle.

(180 − x) = 6.5(90 − x)

180 − x = 585 − 6.5x

5.5x = 405

x = 73.636°

The supplement angle to 73.64° is 106.36°.

The complement angle to 73.64° is 16.36°.

Answer 2

Explanation:

Alright, lets get stared.

Suppose the angle is x.

So, supplement of that angle would be =
`(180-x)`

So, complement of that angle would be =
`(90-x)`

Given that, supplement of an angle is six and a half times as large as the complement of the angle.

`(180-x)=6(1)/(2)(90-x)`

`180-x=6.5(90-x)`

`180-x=585-6.5x`

`6.5x-x=585-180`

`5.5x=405`

`x=73.64`

Hence the angle is 73.64 degrees.

So the measure of its supplement angle would be =
`180-73.64=106.36`

Hence the answer is 106.36 degrees. : Answer

Hope it will help :)