Question

amazing, a 4 week streak...
expressions.
$\angle a = 6x - 2^\circ$ $\angle b = 4x + 48^\circ$
solve for $x$ and then find the measure of $\angle a$:
$\angle a = \square^\circ$

Explanation:

Step1: Identify the relationship between ∠A and ∠B

From the diagram, the two lines are parallel (indicated by the arrows), so ∠A and ∠B are equal (corresponding angles or alternate interior angles, depending on the transversal). So we set \(6x - 2 = 4x + 48\).

Step2: Solve for x

Subtract \(4x\) from both sides: \(6x - 4x - 2 = 48\) → \(2x - 2 = 48\).
Add 2 to both sides: \(2x = 48 + 2\) → \(2x = 50\).
Divide by 2: \(x = \frac{50}{2} = 25\).

Step3: Find the measure of ∠A

Substitute \(x = 25\) into \(∠A = 6x - 2\):
\(∠A = 6(25) - 2 = 150 - 2 = 148\).

Answer:

\(148\)