Question

practice d: (first taught in lesson 17) two angles are a linear pair. one third of the measure of the first plus 12 is equal to the measure of the second. what are the measures of both angles? after you enter your answer press go. and

Explanation:

Step1: Set up equations

Let the first - angle be $x$ and the second - angle be $y$. Since they are a linear pair, $x + y=180$, so $y = 180 - x$. Also, $\frac{1}{3}x+12=y$.

Step2: Substitute $y$ in the second equation

Substitute $y = 180 - x$ into $\frac{1}{3}x + 12=y$, we get $\frac{1}{3}x+12=180 - x$.

Step3: Solve the equation for $x$

Add $x$ to both sides: $\frac{1}{3}x+x+12=180$. Combine like - terms: $\frac{1}{3}x+\frac{3}{3}x+12 = 180$, $\frac{4}{3}x+12=180$. Subtract 12 from both sides: $\frac{4}{3}x=180 - 12=168$. Multiply both sides by $\frac{3}{4}$: $x = 168\times\frac{3}{4}=126$.

Step4: Find the value of $y$

Substitute $x = 126$ into $y = 180 - x$, then $y=180 - 126 = 54$.

Answer:

126, 54