Question

in the figure below, (mangle abd = 112^{circ}), and (mangle1) is (60^{circ}) more than (mangle2). find (mangle2).

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 60$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 112^{\circ}$, we have the equation $x+(x + 60)=112$.

Step2: Simplify the equation

Combining like - terms, we get $2x+60 = 112$.

Step3: Solve for x

Subtract 60 from both sides: $2x=112 - 60$, so $2x = 52$. Then divide both sides by 2: $x=\frac{52}{2}=26$.

Answer:

$26$