Question

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

55
70
35
20

Answer 1

Explanation:

70 is not the correct answer. The complement of 70 is 20 and the supplement of 70 is 110. 70 +110 does not equal 200.

However, the complement of 35 is 55, and the supplement of 35 is 145. 145+55=200

The correct answer is 35

Answer 2

B.
`70^(\circ)`.

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.