Question

∠1 and ∠2 form a linear pair. the measure of ∠2 is six more than twice the measure of ∠1. find m∠2.

Explanation:

Step1: Set up equations

Let $m\angle1 = x$. Since $\angle1$ and $\angle2$ form a linear - pair, $m\angle1 + m\angle2=180^{\circ}$. And we know that $m\angle2 = 2x + 6$. So the equation is $x+(2x + 6)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x+6 = 3x+6$. So the equation becomes $3x + 6=180$.

Step3: Solve for $x$

Subtract 6 from both sides: $3x=180 - 6=174$. Then divide both sides by 3: $x=\frac{174}{3}=58$.

Step4: Find $m\angle2$

Substitute $x = 58$ into the expression for $m\angle2$. Since $m\angle2=2x + 6$, then $m\angle2=2\times58+6=116 + 6=122$.

Answer:

$122$