Question

2.2 | parallel & perpendicular | hw #2
find the m∠1 and m∠2.
134°
1
2
m∠1 =

m∠2 =

Explanation:

Step1: Identify angle - type relationship

The 134 - degree angle and ∠1 are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are congruent.
So, $m\angle1 = 134^{\circ}$.

Step2: Identify supplementary - angle relationship

∠1 and ∠2 are supplementary angles (linear - pair). Supplementary angles add up to 180°.
Let $m\angle2=x$. Then $m\angle1 + x=180^{\circ}$. Substituting $m\angle1 = 134^{\circ}$, we get $134^{\circ}+x = 180^{\circ}$. Solving for $x$, $x=180^{\circ}-134^{\circ}=46^{\circ}$. So, $m\angle2 = 46^{\circ}$.

Answer:

$m\angle1 = 134^{\circ}$
$m\angle2 = 46^{\circ}$