Question

in the figure below, (mangle abd = 115^{circ}), and (mangle2) is (55^{circ}) more than (mangle1). find (mangle1).

Explanation:

Step1: Set up an equation

Let $m\angle1 = x$. Then $m\angle2=x + 55^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 115^{\circ}$, we have the equation $x+(x + 55^{\circ})=115^{\circ}$.

Step2: Simplify the equation

Combine like - terms: $2x+55^{\circ}=115^{\circ}$.

Step3: Solve for x

Subtract $55^{\circ}$ from both sides: $2x=115^{\circ}-55^{\circ}$, so $2x = 60^{\circ}$. Then divide both sides by 2: $x=\frac{60^{\circ}}{2}=30^{\circ}$.

Answer:

$30$