Question

find the value of the variable(s) in each figure. (9x + 12)° 3x° (4y - 10)° x = y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x + 12=3x + 180$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $9x-3x + 12=3x-3x + 180$, which gives $6x+12 = 180$. Then subtract 12 from both sides: $6x+12 - 12=180 - 12$, so $6x=168$. Divide both sides by 6: $x=\frac{168}{6}=2$.

Step3: Use another vertical - angle property

The other pair of vertical angles gives $4y-10 = 3x$.

Step4: Substitute $x$ value and solve for $y$

Substitute $x = 2$ into $4y-10 = 3x$, we get $4y-10=3\times2$. So $4y-10 = 6$. Add 10 to both sides: $4y-10 + 10=6 + 10$, which gives $4y=16$. Divide both sides by 4: $y = 4$.

Answer:

$x = 2$
$y = 10$