Question

given the figure below, find the values of x and z. 61° (8x + 21)° z° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $8x + 21=61$.

Step2: Solve for x

Subtract 21 from both sides of the equation: $8x=61 - 21$, which simplifies to $8x = 40$. Then divide both sides by 8: $x=\frac{40}{8}=5$.

Step3: Use linear - pair property

The angle $z$ and the $61^{\circ}$ angle form a linear - pair (sum to 180°). So, $z + 61=180$.

Step4: Solve for z

Subtract 61 from both sides: $z=180 - 61 = 119$.

Answer:

$x = 5$
$z = 119$