Question

question 4 (2 points)
find m∠1 and m∠2. complete the reasoning.
m∠1 = ____° is a ____ angle with the given.
m∠2 = ____° is a ____ angle with the given.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and the $140^{\circ}$ angle are vertical angles.

Step2: Determine the measure of $\angle1$

Since vertical angles are equal, $m\angle1 = 140^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle2$ and the $140^{\circ}$ angle are supplementary (linear - pair of angles).

Step4: Calculate the measure of $\angle2$

The sum of supplementary angles is $180^{\circ}$. So, $m\angle2=180 - 140=40^{\circ}$.

Answer:

Blank 1: $140$
Blank 2: vertical
Blank 3: $40$
Blank 4: supplementary