Question

in the figure, line m is parallel to line n. if $m\angle3=(7x - 10)^\circ$ and $m\angle6=(5x + 10)^\circ$, what are the measures of $\angle3$ and $\angle6$?

Explanation:

Step1: Identify angle relationship

$\angle 3$ and $\angle 6$ are same-side interior angles, so they are supplementary: $m\angle 3 + m\angle 6 = 180^\circ$

Step2: Substitute angle expressions

$(7x - 10) + (5x + 10) = 180$

Step3: Simplify and solve for $x$

$12x = 180$
$x = \frac{180}{12} = 15$

Step4: Calculate $m\angle 3$

$m\angle 3 = 7(15) - 10 = 105 - 10 = 95$

Step5: Calculate $m\angle 6$

$m\angle 6 = 5(15) + 10 = 75 + 10 = 85$

Answer:

$m\angle 3 = 95^\circ$, $m\angle 6 = 85^\circ$