Question

do now #8: use the same picture
1.) m∠1 = 4x+36 and m∠7= 2x+82. find the measure of x.

Explanation:

Step1: Identify angle - relationship

$\angle1$ and $\angle7$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. So, $m\angle1 = m\angle7$.

Step2: Set up the equation

$4x + 36=2x + 82$.

Step3: Solve for x

Subtract $2x$ from both sides: $4x-2x + 36=2x-2x + 82$, which simplifies to $2x+36 = 82$. Then subtract 36 from both sides: $2x+36 - 36=82 - 36$, getting $2x=46$. Divide both sides by 2: $\frac{2x}{2}=\frac{46}{2}$, so $x = 23$.

Answer:

$x = 23$