Question

in the figure below, (mangle abd = 89^{circ}), and (mangle1) is (19^{circ}) more than (mangle2). find (mangle2).

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 19^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 89^{\circ}$, we have the equation $(x + 19^{\circ})+x=89^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+19^{\circ}=89^{\circ}$.

Step3: Solve for x

Subtract $19^{\circ}$ from both sides: $2x=89^{\circ}-19^{\circ}=70^{\circ}$. Then divide both sides by 2: $x=\frac{70^{\circ}}{2}=35^{\circ}$.

Answer:

$35$