Question

in the figure below, m∠wxz = 66°, and m∠1 is 18° more than m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 18^{\circ}$. Since $m\angle WXZ=m\angle1 + m\angle2$ and $m\angle WXZ = 66^{\circ}$, we have the equation $(x + 18^{\circ})+x=66^{\circ}$.

Step2: Simplify the equation

Combining like - terms, we get $2x+18^{\circ}=66^{\circ}$.

Step3: Solve for $x$

Subtract $18^{\circ}$ from both sides: $2x=66^{\circ}-18^{\circ}=48^{\circ}$. Then divide both sides by 2: $x = 24^{\circ}$.

Answer:

$24$