Question

when two lines intersect, the opposite angles are called vertical angles. vertical angles have equal measures. determine the measures of the vertical angles indicated in the figure to the right. the angles have a measure of

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $2x + 36=8x+6$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $36 = 8x - 2x+6$, which simplifies to $36=6x + 6$. Then subtract 6 from both sides: $36 - 6=6x$, so $30 = 6x$. Divide both sides by 6, we get $x = 5$.

Step3: Find the angle measure

Substitute $x = 5$ into the expression for one of the vertical - angles, say $2x+36$. Then $2\times5+36=10 + 36=46$.

Answer:

$46$