Question

in the figure below, m∠abd = 76°, and m∠1 is three times m∠2. find m∠2

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=3x$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 76^{\circ}$, we have the equation $3x + x=76^{\circ}$.

Step2: Combine like - terms

Combining the left - hand side of the equation $3x + x$, we get $4x=76^{\circ}$.

Step3: Solve for x

Dividing both sides of the equation $4x = 76^{\circ}$ by 4, we have $x=\frac{76^{\circ}}{4}=19^{\circ}$.

Answer:

$19$