Question

given the figure below, find the values of x and z.
(5x - 5)°
(8x - 44)°
z°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x - 5=8x - 44$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $- 5 = 8x-5x - 44$, which simplifies to $-5 = 3x - 44$. Then add 44 to both sides: $3x=-5 + 44$, so $3x = 39$. Divide both sides by 3, we get $x = 13$.

Step3: Find the value of one of the angles

Substitute $x = 13$ into $5x - 5$. So, $5\times13-5=65 - 5=60^{\circ}$.

Step4: Use the linear - pair property to find $z$

Since the angle $(5x - 5)^{\circ}$ and $z^{\circ}$ form a linear - pair (sum to $180^{\circ}$), then $z=180-(5x - 5)$. Substitute $x = 13$, we have $z = 180-60=120^{\circ}$.

Answer:

$x = 13$, $z = 120$