Question

given the figure below, find the values of x and z. 82° (12x + 46)° z° x = 3.5 z = 98

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $12x + 46=82$.

Step2: Solve for x

Subtract 46 from both sides: $12x=82 - 46$, so $12x = 36$. Then divide both sides by 12: $x=\frac{36}{12}=3$.

Step3: Use linear - pair property

The angle $z$ and the $82^{\circ}$ angle form a linear - pair (sum to $180^{\circ}$). So, $z + 82=180$.

Step4: Solve for z

Subtract 82 from both sides: $z=180 - 82 = 98$.

Answer:

$x = 3$, $z = 98$