Question

in the figure below, (mangle wxz = 75^{circ}), and (mangle1) is four times (mangle2). find (mangle2).

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=4x$. Since $m\angle WXZ=m\angle1 + m\angle2$ and $m\angle WXZ = 75^{\circ}$, we have the equation $4x+x=75^{\circ}$.

Step2: Combine like - terms

Combining the left - hand side of the equation $4x+x$, we get $5x = 75^{\circ}$.

Step3: Solve for $x$

Dividing both sides of the equation $5x = 75^{\circ}$ by 5, we have $x=\frac{75^{\circ}}{5}=15^{\circ}$.

Answer:

$15$