given the figure below, find the values of x and z.
given the figure below, find the values of x and z.
Answer
Explanation:
Step1: Use vertical - angle property
Vertical angles are equal. So, $z = 117^{\circ}$ since $z$ and the $117^{\circ}$ angle are vertical angles.
Step2: Set up an equation for $x$
The angle $117^{\circ}$ and $(10x - 27)^{\circ}$ are supplementary (linear - pair), so $117+(10x - 27)=180$. Simplify the left - hand side: $117 + 10x-27=10x + 90$. The equation becomes $10x+90 = 180$. Subtract 90 from both sides: $10x=180 - 90=90$. Divide both sides by 10: $x=\frac{90}{10}=9$.
Answer:
$x = 9$ $z = 117$