Question

in the figure below, m∠abd = 107°, and m∠1 is 43° more than m∠2. find m∠2.

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 43^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 107^{\circ}$, we have the equation $x+(x + 43^{\circ})=107^{\circ}$.

Step2: Simplify the equation

Combining like - terms, we get $2x+43^{\circ}=107^{\circ}$.

Step3: Solve for x

Subtract $43^{\circ}$ from both sides: $2x=107^{\circ}- 43^{\circ}=64^{\circ}$. Then divide both sides by 2: $x=\frac{64^{\circ}}{2}=32^{\circ}$.

Answer:

$32$