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aliina [53]
3 years ago
10

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

Mathematics
1 answer:
AlexFokin [52]3 years ago
8 0

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.

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