Question

given the figure below, find the values of x and z. (5x + 62)° (9x + 48)° z° x = z =

Explanation:

Step1: Set up equation for x

The two given angles $(5x + 62)^{\circ}$ and $(9x+48)^{\circ}$ are vertical angles, so they are equal. Set up the equation $5x + 62=9x + 48$.
$5x+62 = 9x + 48$

Step2: Solve for x

Subtract $5x$ from both sides: $62=4x + 48$. Then subtract 48 from both sides: $14 = 4x$. Divide both sides by 4: $x=\frac{14}{4}=\frac{7}{2}=3.5$.
$62-48=4x$
$14 = 4x$
$x = 3.5$

Step3: Find the value of z

The angle $z^{\circ}$ and $(5x + 62)^{\circ}$ are supplementary (a linear - pair), so $z+(5x + 62)=180$. Substitute $x = 3.5$ into the equation: $z+(5\times3.5+62)=180$. First, calculate $5\times3.5+62=17.5 + 62=79.5$. Then $z=180 - 79.5 = 100.5$.
$z=180-(5\times3.5 + 62)$
$z=180 - 79.5$
$z = 100.5$

Answer:

$x = 3.5$
$z = 100.5$