Question

in the figure below, m∠abd = 118°, and m∠2 is 72° more than m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 72^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 118^{\circ}$, we have the equation $x+(x + 72^{\circ})=118^{\circ}$.

Step2: Simplify the left - hand side

Combining like terms, we get $2x+72^{\circ}=118^{\circ}$.

Step3: Solve for $x$

Subtract $72^{\circ}$ from both sides: $2x=118^{\circ}-72^{\circ}$, so $2x = 46^{\circ}$. Then divide both sides by 2: $x=\frac{46^{\circ}}{2}=23^{\circ}$.

Answer:

$23$