Question

example: if m∠3=(4x+7)° and m∠6=(5x - 13)°, find the value of x. check: find the value of y if m∠8=68° and m∠3=(3y - 2)°.

Explanation:

Step1: Identify angle - relationship

Assume that $\angle3$ and $\angle6$ are alternate - interior angles (if lines are parallel), so they are equal. Set up the equation $4x + 7=5x - 13$.
$4x+7 = 5x - 13$

Step2: Solve for x

Subtract $4x$ from both sides: $7=x - 13$.
$7=x - 13$
Then add 13 to both sides: $x=20$.

For the check part:

Step1: Identify angle - relationship

Assume that $\angle8$ and $\angle3$ are corresponding angles (if lines are parallel), so they are equal. Set up the equation $3y-2 = 68$.
$3y-2=68$

Step2: Solve for y

Add 2 to both sides: $3y=70$.
$3y = 70$
Then divide both sides by 3: $y=\frac{70}{3}$.

Answer:

For the example, $x = 20$. For the check, $y=\frac{70}{3}$.