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

Answer:

Option C.

Step-by-step explanation:

Let the angle is x

Then the supplement of the angle is 180-x

And complement is: 90-x

We have been given that the The supplement of an angle is six and a half times as large as the complement of the angle.

Thus the equation becomes:

$180-x=6\frac{1}{2}(90-x)$

$180-x=\frac{13}{2}(90-x)$

$180-x=13\cdot 45-\frac{13}{2}x$

$\frac{-11x}{2}=-405$

$\Rightarrow x=73.63$

We need to calculate the supplement  angle which is:

$180-73.63=106.37$

Therefore, option C is correct.

Answer 2

Answer:

106.63

Step-by-step 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°.