Question

in the figure below, (mangle abd = 75^{circ}), and (mangle 2) is two times (mangle 1). find (mangle 1).

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=2x$. Since $m\angle ABD=m\angle1 + m\angle2$, we have $x + 2x=75^{\circ}$.

Step2: Solve the equation

Combining like - terms, $3x = 75^{\circ}$. Dividing both sides by 3, we get $x=\frac{75^{\circ}}{3}=25^{\circ}$.

Answer:

$25$