Question

1. solve for the missing variables.

Explanation:

Step1: Use angle - sum property on the lower - level angles

The sum of angles on a straight line is 180°. So, \(2x + 90+x=180\).
Combining like terms, we get \(3x + 90=180\).
Subtract 90 from both sides: \(3x=180 - 90\), so \(3x = 90\).
Divide both sides by 3: \(x=\frac{90}{3}=30\).

Step2: Use vertical - angle property

The angle \(2y\) and the angle \(x\) are vertical angles. Vertical angles are equal. So \(2y=x\).
Since \(x = 30\), then \(2y=30\), and \(y=\frac{30}{2}=15\).

Step3: Use corresponding - angle property

The angle \(z\) and the angle \(2x\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.
Since \(x = 30\), then \(2x=60\), so \(z = 60\).

Answer:

\(x = 30\), \(y = 15\), \(z = 60\)