Question

1. given the figure below, find the values of x and z. (1pt)

(a) x =
(b) z =
(8x + 1)°
65°
z°

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, $8x + 1=65$.

Step2: Solve for $x$

Subtract 1 from both sides of the equation: $8x=65 - 1=64$. Then divide both sides by 8, so $x=\frac{64}{8}=8$.

Step3: Use linear - pair property

The angle $z$ and the $65^{\circ}$ angle form a linear - pair. So, $z + 65=180$.

Step4: Solve for $z$

Subtract 65 from both sides of the equation: $z=180 - 65 = 115$.

Answer:

(a) $x = 8$
(b) $z = 115$