Question

in the figure below, m∠abd = 114°, and m∠1 is 38° more than m∠2. find m∠2.

Explanation:

Step1: Set up the relationship

Let $m\angle2 = x$. Then $m\angle1=x + 38^{\circ}$.

Step2: Use the angle - sum property

Since $m\angle ABD=m\angle1 + m\angle2$ and $m\angle ABD = 114^{\circ}$, we have the equation $(x + 38^{\circ})+x=114^{\circ}$.

Step3: Simplify the equation

Combining like - terms, we get $2x+38^{\circ}=114^{\circ}$.

Step4: Solve for $x$

Subtract $38^{\circ}$ from both sides: $2x=114^{\circ}-38^{\circ}=76^{\circ}$. Then divide both sides by 2: $x=\frac{76^{\circ}}{2}=38^{\circ}$.

Answer:

$38$