Question

∠1 and ∠2 are vertical angles. if (mangle1=(4x + 2)^{circ}) and (mangle2=(x + 17)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $4x + 2=x + 17$.

Step2: Solve for $x$

Subtract $x$ from both sides: $4x - x+2=x - x + 17$, which simplifies to $3x+2 = 17$. Then subtract 2 from both sides: $3x+2 - 2=17 - 2$, getting $3x=15$. Divide both sides by 3: $\frac{3x}{3}=\frac{15}{3}$, so $x = 5$.

Step3: Find the measure of $\angle2$

Substitute $x = 5$ into the expression for $m\angle2$. $m\angle2=(x + 17)^{\circ}=(5 + 17)^{\circ}=22^{\circ}$.

Answer:

$22^{\circ}$