Question

in the figure below, m∠abd = 96°, and m∠1 is 56° more than m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 56^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 96^{\circ}$, we have the equation $x+(x + 56^{\circ})=96^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+56^{\circ}=96^{\circ}$.

Step3: Solve for x

Subtract $56^{\circ}$ from both sides: $2x=96^{\circ}-56^{\circ}$, so $2x = 40^{\circ}$. Then divide both sides by 2: $x=\frac{40^{\circ}}{2}=20^{\circ}$.

Answer:

$20$