Question

hw 2/9 - parallel lines and transversals
if line l is parallel to line m, $m\angle1 = (6x + 5)^\circ$, and $m\angle2 = (9x - 46)^\circ$, find $m\angle1$.
$m\angle1 = \square$

Explanation:

Step1: Identify congruent angles

Since line $l \parallel$ line $m$, $\angle 1 \cong \angle 2$, so $m\angle 1 = m\angle 2$.

Step2: Set up equation

$$6x + 5 = 9x - 46$$

Step3: Solve for $x$

$$5 + 46 = 9x - 6x$$
$$51 = 3x$$
$$x = \frac{51}{3} = 17$$

Step4: Calculate $m\angle 1$

Substitute $x=17$ into $m\angle 1 = 6x + 5$:
$$m\angle 1 = 6(17) + 5 = 102 + 5$$

Answer:

$107^\circ$