Question

(d) problem 20: 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, $x + y=180^{\circ}$, so $y = 180 - x$. Also, $\frac{x}{2}+9=y$.

Step2: Substitute and solve

Substitute $y = 180 - x$ into $\frac{x}{2}+9=y$, we get $\frac{x}{2}+9=180 - x$. Add $x$ to both sides: $\frac{x}{2}+x+9=180$. Combine like - terms: $\frac{x + 2x}{2}+9=180$, $\frac{3x}{2}+9=180$. Subtract 9 from both sides: $\frac{3x}{2}=180 - 9=171$. Multiply both sides by $\frac{2}{3}$: $x=\frac{2\times171}{3}=108^{\circ}$.

Step3: Find the second angle

Substitute $x = 108^{\circ}$ into $y = 180 - x$, then $y=180 - 108 = 72^{\circ}$.

Answer:

$108^{\circ}, 72^{\circ}$