Question

in the figure below, m∠abd = 110°, and m∠2 is four times m∠1. find m∠1.

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Since $m\angle2$ is four times $m\angle1$, then $m\angle2 = 4x$. And we know that $m\angle ABD=m\angle1 + m\angle2$, so $x + 4x=110$.

Step2: Solve the equation

Combining like - terms in the equation $x + 4x=110$, we get $5x = 110$. Then, dividing both sides of the equation by 5, we have $x=\frac{110}{5}=22$.

Answer:

$22$