Question

in the figure below, $mangle wxz = 91^{circ}$, and $mangle1$ is $13^{circ}$ more than $mangle2$. find $mangle2$.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 13$. Since $m\angle WXZ=m\angle1 + m\angle2$ and $m\angle WXZ = 91^{\circ}$, we have the equation $x+(x + 13)=91$.

Step2: Simplify the equation

Combine like - terms: $2x+13 = 91$.

Step3: Solve for x

Subtract 13 from both sides: $2x=91 - 13=78$. Then divide both sides by 2: $x=\frac{78}{2}=39$.

Answer:

$39$