Question

in the figure below, m∠abd = 96°, and m∠1 is two times m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1 = 2x$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 96^{\circ}$, we have the equation $2x+x=96^{\circ}$.

Step2: Combine like - terms

Combining the left - hand side of the equation $2x+x$, we get $3x = 96^{\circ}$.

Step3: Solve for x

Dividing both sides of the equation $3x = 96^{\circ}$ by 3, we have $x=\frac{96^{\circ}}{3}=32^{\circ}$.

Answer:

$32$