Question

in the figure below, m∠wxz = 77°, and m∠2 is 25° more than m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 25^{\circ}$. Since $m\angle WXZ=m\angle1 + m\angle2$ and $m\angle WXZ = 77^{\circ}$, we have the equation $x+(x + 25^{\circ})=77^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+25^{\circ}=77^{\circ}$.

Step3: Solve for x

Subtract $25^{\circ}$ from both sides: $2x=77^{\circ}-25^{\circ}=52^{\circ}$. Then divide both sides by 2: $x=\frac{52^{\circ}}{2}=26^{\circ}$.

Answer:

$26$