Question

in the figure below, m∠abd = 92°, and m∠2 is 8° more than m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 8$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 92^{\circ}$, we have the equation $x+(x + 8)=92$.

Step2: Simplify the equation

Combine like - terms: $2x+8 = 92$.

Step3: Solve for x

Subtract 8 from both sides: $2x=92 - 8=84$. Then divide both sides by 2: $x=\frac{84}{2}=42$.

Answer:

$42$