Question

in the figure below, m∠abd = 71°, and m∠2 is 13° more than m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 13$. Since $m\angle ABD=m\angle1+m\angle2$ and $m\angle ABD = 71^{\circ}$, we have the equation $x+(x + 13)=71$.

Step2: Simplify the left - hand side

Combining like terms, $x+(x + 13)$ simplifies to $2x+13$. So the equation becomes $2x+13 = 71$.

Step3: Solve for x

Subtract 13 from both sides: $2x+13-13=71 - 13$, which gives $2x=58$. Then divide both sides by 2: $\frac{2x}{2}=\frac{58}{2}$, so $x = 29$.

Answer:

$29$