Question

what are the values of x, y, and z? use theorems to justify each answer. by the angles theorem and the triangle theorem, x = (type a whole number.)

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle vertical to the \(60^{\circ}\) angle is also \(60^{\circ}\).

Step2: Use the angle - sum property of a triangle

In a triangle formed by the angles \(x\), \(14^{\circ}\), and the \(60^{\circ}\) (vertical - angle), the sum of interior angles of a triangle is \(180^{\circ}\). So \(x + 14^{\circ}+60^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

$$
LATEXBLOCK0
$$

Step4: Find \(y\)

\(y\) and the \(14^{\circ}\) angle are vertical angles. So \(y = 14\).

Step5: Find \(z\)

\(z\) and the \(60^{\circ}\) angle are vertical angles. So \(z = 60\).

Answer:

\(x = 106\), \(y = 14\), \(z = 60\)