Question

given the figure below, find the values of x and z. (10x - 91)° z° (6x - 27)° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $10x - 91=6x - 27$.

Step2: Solve for x

Subtract $6x$ from both sides: $10x-6x - 91=6x-6x - 27$, which simplifies to $4x-91=-27$. Then add 91 to both sides: $4x-91 + 91=-27 + 91$, so $4x = 64$. Divide both sides by 4: $x=\frac{64}{4}=16$.

Step3: Find the measure of one angle

Substitute $x = 16$ into $6x - 27$. We get $6\times16-27=96 - 27 = 69$.

Step4: Use linear - pair property

The angle with measure $z$ and the angle with measure $6x - 27$ (which is 69 degrees) form a linear - pair. So $z+69 = 180$. Then $z=180 - 69=111$.

Answer:

$x = 16$
$z = 111$