Question

use the given information to find m∠a. m∠d = 117°, m∠a=(2x)°, m∠b=(x + 37.5)°. m∠a=□° (the figure is not drawn to scale.)

Explanation:

Step1: Assume angles relationship

Since we assume that $\angle A$ and $\angle D$ are vertical - angles (a common relationship in intersection of lines), vertical angles are equal. So $m\angle A=m\angle D$.

Step2: Set up the equation

We know that $m\angle A=(2x)^{\circ}$ and $m\angle D = 117^{\circ}$, so $2x=117$.

Step3: Solve for $x$

Divide both sides of the equation $2x = 117$ by 2. We get $x=\frac{117}{2}=58.5$.

Step4: Find $m\angle A$

Since $m\angle A=(2x)^{\circ}$, substitute $x = 58.5$ into the expression. Then $m\angle A=2\times58.5^{\circ}=117^{\circ}$.

Answer:

$117$