Question

m∠6 is (2x - 5)° and m∠8 is (x + 5)°. what is m∠3?

Explanation:

Step1: Identify angle - relationship

Since $\angle6$ and $\angle8$ are vertical - angles, they are congruent. So, $2x - 5=x + 5$.

Step2: Solve for $x$

Subtract $x$ from both sides of the equation: $2x-x-5=x - x+5$, which simplifies to $x - 5 = 5$. Then add 5 to both sides: $x=5 + 5=10$.

Step3: Find the measure of $\angle6$

Substitute $x = 10$ into the expression for $m\angle6$: $m\angle6=2x-5=2\times10 - 5=20 - 5 = 15^{\circ}$.

Step4: Identify the relationship between $\angle6$ and $\angle3$

$\angle6$ and $\angle3$ are alternate - interior angles. Since lines $q$ and $s$ are parallel, $m\angle3=m\angle6$.

Answer:

$15$