Question

two angles are a linear pair. half the measure of the first plus 9 is equal to the measure of the second. what are the measures of both angles? after you enter your answer press go.

Explanation:

Step1: Set up equations

Let the first - angle be $x$ and the second - angle be $y$. Since they are a linear pair, $x + y=180$ (linear - pair angles are supplementary). Also, $\frac{x}{2}+9 = y$.

Step2: Substitute $y$ in the first equation

Substitute $y=\frac{x}{2}+9$ into $x + y=180$. We get $x+\frac{x}{2}+9 = 180$.

Step3: Simplify the equation

Combine like terms: $\frac{2x + x}{2}+9 = 180$, which is $\frac{3x}{2}+9 = 180$. Subtract 9 from both sides: $\frac{3x}{2}=180 - 9=171$.

Step4: Solve for $x$

Multiply both sides by $\frac{2}{3}$: $x = 171\times\frac{2}{3}=114\times2 = 84$.

Step5: Solve for $y$

Substitute $x = 84$ into $y=\frac{x}{2}+9$. Then $y=\frac{84}{2}+9=42 + 9=96$.

Answer:

84, 96