Question

find the values of x and y. (3x - 16)° y° (5x - 110)° x = y = need help with this question? previous

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $3x - 16=5x - 110$.

Step2: Solve for x

Subtract $3x$ from both sides: $-16 = 5x-3x - 110$.
Simplify to get $-16 = 2x - 110$.
Add 110 to both sides: $-16 + 110=2x$, so $94 = 2x$.
Divide both sides by 2: $x=\frac{94}{2}=47$.

Step3: Find y

Since $y$ and $(3x - 16)$ are supplementary (linear - pair of angles), $y+(3x - 16)=180$.
Substitute $x = 47$ into $3x - 16$: $3\times47-16=141 - 16 = 125$.
Then $y=180-(3x - 16)=180 - 125 = 55$.

Answer:

$x = 47$
$y = 55$