Question

the angle measurements in the diagram are represented by the following expressions. $angle a = 5x - 15^{circ}$ $angle b = 2x + 21^{circ}$ solve for $x$ and then find the measure of $angle b$: $angle b = square^{circ}$

Explanation:

Step1: Set up the equation

Since \( \angle A \) and \( \angle B \) are alternate - interior angles (because the lines are parallel and cut by a transversal), \( \angle A=\angle B \). So, \( 5x - 15=2x + 21 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 5x-2x - 15=2x-2x + 21 \), which gives \( 3x-15 = 21 \).
Add \( 15 \) to both sides: \( 3x-15 + 15=21 + 15 \), so \( 3x=36 \).
Divide both sides by \( 3 \): \( x=\frac{36}{3}=12 \).

Step3: Find the measure of \( \angle B \)

Substitute \( x = 12 \) into the expression for \( \angle B \): \( \angle B=2x + 21 \).
\( \angle B=2\times12 + 21=24 + 21=45 \).

Answer:

\( 45 \)