Question

in the figure below, (mangle abd = 89^{circ}), and (mangle 2) is (41^{circ}) more than (mangle 1). find (mangle 1).

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 41^{\circ}$. Since $m\angle ABD=90^{\circ}$ and $\angle ABD=\angle1+\angle2$, we have the equation $x+(x + 41^{\circ})=90^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+41^{\circ}=90^{\circ}$.

Step3: Solve for x

Subtract $41^{\circ}$ from both sides: $2x=90^{\circ}-41^{\circ}=49^{\circ}$. Then divide both sides by 2: $x=\frac{49^{\circ}}{2}=24.5^{\circ}$.

Answer:

$24.5$