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.) m∠a=□°

Explanation:

Step1: Identify angle - relationship

Assume angles $\angle A$ and $\angle B$ are vertical - angles (since no other information about their relationship is given and vertical angles are often considered in such problems). Vertical angles are equal, so $m\angle A=m\angle B$.

Step2: Set up the equation

We know that $m\angle A = 2x$ and $m\angle B=x + 30.5$. So, $2x=x + 30.5$.

Step3: Solve the equation for $x$

Subtract $x$ from both sides of the equation $2x=x + 30.5$. We get $2x−x=x + 30.5−x$, which simplifies to $x = 30.5$.

Step4: Find $m\angle A$

Since $m\angle A = 2x$, substitute $x = 30.5$ into the expression. Then $m\angle A=2\times30.5=61$.

Answer:

$61$