Question

question 6 of 6
$m\angle5 = 8x - 15$
$m\angle3 = 6x + 3$
what is the measure of $\angle3$?

Explanation:

Step1: Analyze the relationship between angles

Since the two lines are parallel, $\angle3$ and $\angle5$ are alternate - interior angles. So, $m\angle3 = m\angle5$.

Step2: Set up the equation

Given $m\angle3=6x + 3$ and $m\angle5=8x-15$. Then $6x + 3=8x-15$.

Step3: Solve the equation for $x$

Subtract $6x$ from both sides: $3=2x - 15$.
Add $15$ to both sides: $18 = 2x$.
Divide by $2$: $x = 9$.

Step4: Find the measure of $\angle3$

Substitute $x = 9$ into $m\angle3=6x + 3$.
$m\angle3=6\times9+3=54 + 3=57$.

Answer:

$57$