Question

in the figure below, m∠abd = 65°, and m∠1 is 17° more than m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 17^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 65^{\circ}$, we have the equation $x+(x + 17^{\circ})=65^{\circ}$.

Step2: Simplify the equation

Combining like - terms, we get $2x+17^{\circ}=65^{\circ}$.

Step3: Solve for $x$

Subtract $17^{\circ}$ from both sides: $2x=65^{\circ}-17^{\circ}=48^{\circ}$. Then divide both sides by 2: $x=\frac{48^{\circ}}{2}=24^{\circ}$.

Answer:

$24$