Question

practice problems. solve for the given variable and justify.
a. diagram with angles 2x + 20° and 5x - 10°
b. diagram with angles 5x + 10° and 3x + 30°

Explanation:

Part a

Step1: Identify angle relationship

The two angles \(2x + 20^\circ\) and \(5x - 10^\circ\) are alternate interior angles (since lines are parallel, alternate interior angles are equal). So set them equal: \(2x + 20 = 5x - 10\).

Step2: Solve for x

Subtract \(2x\) from both sides: \(20 = 3x - 10\). Add 10 to both sides: \(30 = 3x\). Divide by 3: \(x = 10\).

Step1: Identify angle relationship

The angles \(5x + 10^\circ\) and \(3x + 30^\circ\) are alternate interior angles (parallel lines, so they are equal). Set equal: \(5x + 10 = 3x + 30\).

Step2: Solve for x

Subtract \(3x\) from both sides: \(2x + 10 = 30\). Subtract 10: \(2x = 20\). Divide by 2: \(x = 10\).

Answer:

\(x = 10\)

Part b