Question

The sum of the measures of a complement and a supplement of an angle is 200. What is the measure of the angle?

Answer 1

Answer:

B. $70^{\circ}$.

Step-by-step explanation:

Let x be the required angle and y be its complement and z be its supplement.

We have been given that the sum the measures of a complement and a supplement of an angle is 200.

$x+y+z=200^{\circ}...(1)$

We know that complementary angles add up-to 90 degrees, so we can set an equation as:

$x+y=90^{\circ}...(2)$

We know that supplementary angles add up-to 180 degrees, so we can set an equation as:

$x+z=180^{\circ}....(3)$

We will use substitution method to solve our given equation. From equation (2) and (3) we will get,

$y=90^{\circ}-x$

$z=180^{\circ}-x$

Substituting these values in equation (1) we will get,

$x+90^{\circ}-x+180^{\circ}-x=200^{\circ}$

Combine like terms:

$-x+270^{\circ}=200^{\circ}$

$-x+270^{\circ}-270^{\circ}=200^{\circ}-270^{\circ}$

$-x=-70^{\circ}$

$x=70^{\circ}$

Therefore, the measure of the required angle is 70 degrees and option B is the correct choice.