Question

select the answer to each question below.

1. the supplement of an angle is 4 times as large as the angle. find the angle.
2. add 27 to the measure of an angle, and the result is half of the angle’s supplement. what is the measure of the angle?

Explanation:

Step1: Let the angle be $x$.

The supplement of the angle is $180 - x$.

Step2: Solve problem 21

Given that the supplement of an angle is 4 times as large as the angle. So we have the equation $180 - x=4x$.
Add $x$ to both sides: $180 = 4x+x$.
Combine like - terms: $180 = 5x$.
Divide both sides by 5: $x=\frac{180}{5}=36$.

Step3: Solve problem 22

Let the angle be $y$. Its supplement is $180 - y$.
The equation based on the problem is $y + 27=\frac{1}{2}(180 - y)$.
Multiply both sides by 2 to get rid of the fraction: $2(y + 27)=180 - y$.
Expand the left - hand side: $2y+54 = 180 - y$.
Add $y$ to both sides: $2y + y+54=180$.
Combine like - terms: $3y+54 = 180$.
Subtract 54 from both sides: $3y=180 - 54$.
$3y = 126$.
Divide both sides by 3: $y = 42$.

Answer:

1. 36
2. 42