Question

in the figure below, m∠abd = 115°, and m∠1 is four times m∠2. find m∠2.

Explanation:

Step1: Set up the relationship

Let $m\angle2 = x$. Then $m\angle1 = 4x$.

Step2: Use angle - addition property

Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 115^{\circ}$, we have the equation $4x+x=115^{\circ}$.

Step3: Solve the equation

Combining like - terms, $5x = 115^{\circ}$. Then $x=\frac{115^{\circ}}{5}=23^{\circ}$.

Answer:

$23$