Question

1. ∠1 and ∠2 form vertical angles. ∠1=(5x)°, ∠2=(x+16)°.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( \angle1=\angle2 \).

Step2: Set up the equation

Given \( \angle1 = (5x)^\circ \) and \( \angle2=(x + 16)^\circ \), we have \( 5x=x + 16 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( 5x-x=x + 16-x \), which simplifies to \( 4x=16 \). Then divide both sides by 4: \( x=\frac{16}{4}=4 \).

Step4: Find the measure of angles

Substitute \( x = 4 \) into \( \angle1 \): \( \angle1=5\times4 = 20^\circ \). Check with \( \angle2 \): \( \angle2=4 + 16=20^\circ \), which confirms they are equal.

Answer:

The value of \( x \) is \( 4 \), and the measure of each angle ( \( \angle1 \) and \( \angle2 \)) is \( 20^\circ \).