Question

1. the measure of the supplement of an angle is 60 less than 3 times the measure of the complement of an angle. find the measure of the complement.

Explanation:

Step1: Let the angle be $x$.

The supplement of the angle is $180 - x$, and the complement of the angle is $90 - x$.

Step2: Set up the equation.

We are given that $180 - x=3(90 - x)-60$.

Step3: Expand and solve the equation.

Expand the right - hand side: $180 - x = 270-3x - 60$.
Combine like terms: $180 - x=210 - 3x$.
Add $3x$ to both sides: $180 - x+3x=210 - 3x+3x$, which gives $180 + 2x=210$.
Subtract 180 from both sides: $2x=210 - 180$, so $2x = 30$.
Divide both sides by 2: $x = 15$.

Step4: Find the measure of the complement.

The complement of the angle $x$ is $90 - x$. Substitute $x = 15$ into it, we get $90-15 = 75$.

Answer:

75