Question

43° (13x + 1)° (7x + 19)° find m∠y

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $13x + 1=7x + 19$.

Step2: Solve the equation for $x$

Subtract $7x$ from both sides: $13x-7x + 1=7x-7x + 19$, which simplifies to $6x+1 = 19$. Then subtract 1 from both sides: $6x+1 - 1=19 - 1$, getting $6x=18$. Divide both sides by 6: $x=\frac{18}{6}=3$.

Step3: Find the measure of one of the vertical - angles

Substitute $x = 3$ into $13x + 1$. We have $13\times3+1=39 + 1=40^{\circ}$.

Step4: Use the linear - pair property to find $m\angle y$

The angle with measure $43^{\circ}$ and $\angle y$ and the vertical - angle (which is $40^{\circ}$) form a straight - line. The sum of angles on a straight - line is $180^{\circ}$. So, $m\angle y=180-(43 + 40)$.
$m\angle y=180 - 83=97^{\circ}$.

Answer:

$97^{\circ}$