Question

given m || n, find the value of x and y. (6x + 13)° y° (7x - 5)°

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, we have $6x + 13=7x - 5$.

Step2: Solve for $x$

Subtract $6x$ from both sides: $13=x - 5$. Then add 5 to both sides, we get $x = 18$.

Step3: Find the value of $y$

The angle $(6x + 13)^{\circ}$ and $y^{\circ}$ are supplementary (linear - pair of angles). First, find the value of $6x+13$ when $x = 18$. $6x+13=6\times18 + 13=108+13 = 121$. Since the sum of angles in a linear - pair is $180^{\circ}$, then $y=180-(6x + 13)$. Substitute $x = 18$ into the equation, $y = 180-121=59$.

Answer:

$x = 18$
$y = 59$