Answer:
49°
Step-by-step explanation:
We are given:
m∠1 = 50°
m∠2 = 48°
Since m║n and s bisects ∠ABC (this means that line s cuts the angle in half) and as you can see, the line extends, bisecting the angle across it.
We have this theorem about corresponding angles, when a line transverses across two parallel lines. ∠ABC corresponds to the angle that ∠3 is a part of. Look at the picture to see what I am referring to. The red lines show the corresponding angles.
m∠1 and m∠2 summed up would be equal to the measure of ∠ABC.
m∠1 = 50°
m∠2 = 48°
m∠1 + m∠2 = ∠ABC
50° + 48° = ∠ABC
98° = ∠ABC
This means that the corresponding angle is also equal to 98°.
Now since the s bisects the corresponding angle forming ∠3, we just divide the measure of the angle by 2 and we have your answer:
m∠3 = 98°/2
m∠3 = 49°
