Question

use the given information to find m∠a. m∠d = 119°, m∠a=(2x)°, m∠b=(x + 30.5)°. (the figure is not drawn to scale)

Explanation:

Step1: Set up the equation

Since $\angle A=(2x)^{\circ}$ and we are given that $m\angle A = 61^{\circ}$, we have the equation $2x=61$.

Step2: Solve for $x$

Divide both sides of the equation $2x = 61$ by 2. So $x=\frac{61}{2}=30.5$.
We can also check the information about $\angle B=(x + 30.5)^{\circ}$. Substituting $x = 30.5$ into the expression for $\angle B$, we get $m\angle B=(30.5+30.5)^{\circ}=61^{\circ}$. But we were already directly given that $m\angle A = 61^{\circ}$.

Answer:

$61^{\circ}$