Question

given the figure below, find the values of x and z.
109°
z °
(11x − 78)°
x = □
z = □

Explanation:

Step1: Identify Vertical Angles

Vertical angles are equal. So, \(11x - 78 = 109\).

Step2: Solve for \(x\)

Add 78 to both sides: \(11x = 109 + 78\)
\(11x = 187\)
Divide by 11: \(x = \frac{187}{11}\)
\(x = 17\)

Step3: Find \(z\) (Supplementary Angles)

\(z\) and \(109^\circ\) are supplementary (sum to \(180^\circ\)): \(z + 109 = 180\)
\(z = 180 - 109\)
\(z = 71\)

Answer:

\(x = 17\)
\(z = 71\)