Question

∠1 and ∠2 are vertical angles. if m∠1=(3x - 29)° and m∠2=(2x + 3)°, then find the measure of ∠2.

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $3x - 29=2x + 3$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $3x-2x-29=2x - 2x+ 3$, which simplifies to $x-29 = 3$. Then add 29 to both sides: $x=3 + 29$, so $x = 32$.

Step3: Find measure of $\angle2$

Substitute $x = 32$ into the expression for $m\angle2$. $m\angle2=(2\times32 + 3)^{\circ}=(64 + 3)^{\circ}=67^{\circ}$.

Answer:

$67^{\circ}$