Question

in the figure below, (mangle abd = 72^{circ}), and (mangle1) is (14^{circ}) more than (mangle2). find (mangle2).

Explanation:

Step1: Set up an equation

Let $m\angle2 = x$. Then $m\angle1=x + 14^{\circ}$. Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 72^{\circ}$, we have the equation $(x + 14^{\circ})+x=72^{\circ}$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $2x+14^{\circ}=72^{\circ}$.

Step3: Isolate the variable

Subtract $14^{\circ}$ from both sides: $2x=72^{\circ}-14^{\circ}=58^{\circ}$.

Step4: Solve for $x$

Divide both sides by 2: $x=\frac{58^{\circ}}{2}=29^{\circ}$.

Answer:

$m\angle2 = 29^{\circ}$