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 $74^{\circ}$ angle is also $74^{\circ}$.

Step2: Use triangle - angle sum theorem

In the triangle formed, the sum of interior angles of a triangle is $180^{\circ}$. One angle in the triangle is $65^{\circ}$ and another is $74^{\circ}$. Let the third angle be $x$. Then $x=180-(74 + 65)$.
$x=180 - 139=41$.

Answer:

$x = 41$