Question

2.7.29 hw score: 40% 14 of 35 points o points: 0 of 1 (4x - 33)° (6y - x - 12) (x + 12)°

Explanation:

Step1: Identify Vertical Angles

Angles \((4x - 33)^\circ\) and \((x + 12)^\circ\) are vertical angles, so they are equal.

$$4x - 33 = x + 12$$

Step2: Solve for \(x\)

Subtract \(x\) from both sides:

$$3x - 33 = 12$$

Add 33 to both sides:

$$3x = 45$$

Divide by 3:

$$x = 15$$

Step3: Find Angle Measure

Substitute \(x = 15\) into \((x + 12)^\circ\):

$$15 + 12 = 27^\circ$$

Now, angles \((4x - 33)^\circ\) and \((6y - x - 12)^\circ\) are supplementary (linear pair). First, find \((4x - 33)^\circ\) with \(x = 15\):

$$4(15) - 33 = 60 - 33 = 27^\circ$$

So, \((6y - x - 12)^\circ = 180 - 27 = 153^\circ\). Substitute \(x = 15\):

$$6y - 15 - 12 = 153$$

$$6y - 27 = 153$$

Add 27:

$$6y = 180$$

Divide by 6:

$$y = 30$$

Answer:

\(x = 15\), \(y = 30\) (If the question was to find \(x\) and \(y\); adjust based on actual question, but steps show solving for \(x\) and \(y\) using vertical angles and supplementary angles.)