Question

1. ∠1 and ∠2 are vertical angles. if m∠1 = (5x 12)° and m∠2 = (6x - 11)°, find m∠1.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).
Given \( m\angle1=(5x - 12)^\circ \) and \( m\angle2=(6x - 11)^\circ \), we set up the equation:
\( 5x - 12 = 6x - 11 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( -12 = x - 11 \)
Add 11 to both sides:
\( x = -1 \)

Step3: Find \( m\angle1 \)

Substitute \( x = -1 \) into \( m\angle1=(5x - 12)^\circ \):
\( m\angle1 = 5(-1) - 12 = -5 - 12 = -17 \)? Wait, that can't be right. Wait, maybe there's a typo in the problem. Wait, maybe \( m\angle1=(5x + 12)^\circ \)? Let's assume that (since angle measure can't be negative). Let's correct the equation:

If \( m\angle1=(5x + 12)^\circ \) and \( m\angle2=(6x - 11)^\circ \), then:

\( 5x + 12 = 6x - 11 \)

Subtract \( 5x \): \( 12 = x - 11 \)

Add 11: \( x = 23 \)

Then \( m\angle1 = 5(23) + 12 = 115 + 12 = 127^\circ \)

Wait, the original problem has \( (5x 12)^\circ \), maybe it's \( (5x + 12)^\circ \). Let's proceed with that correction.

Answer:

\( 127^\circ \) (assuming the angle is \( (5x + 12)^\circ \) instead of \( (5x - 12)^\circ \) to get a positive angle measure)