Question

in the figure below, m∠abd = 97°, and m∠2 is 29° more than m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 29^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 97^{\circ}$, we have the equation $x+(x + 29^{\circ})=97^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+29^{\circ}=97^{\circ}$.

Step3: Solve for x

Subtract $29^{\circ}$ from both sides: $2x=97^{\circ}-29^{\circ}=68^{\circ}$. Then divide both sides by 2: $x=\frac{68^{\circ}}{2}=34^{\circ}$.

Answer:

$34$