Answer:
m<1 = 62°
m<2 = 45°
m<3 = 24°
Explanation:
Hi!
Let me walk you through it!
The first step is to find angle 1.
Angle 1 is supplementary with the angle 118°
So we do 180° - 118° = 62°
m<1 = 62°
Then we find angle 2.
There are two ways to do this
The sum of interior angles in a triangle is 180°
So we do 180° - (73 + 62°)
Open parenthesis:
180° - 73° - 62° = 45°
You can also use the exterior angle theorem
118° = 73° + m<2
Same to both sides:
45° = m<2
So
m<2 = 45°
Now, using this information, we can find angle measure 3.
Now we look at the big triangle. Again, there are two ways to do this.
First way:
m<1 + 49° + m<2 + m<3 = 180°
Plug in known-values
62° + 49° + 45° + m<3 = 180°
Combine like terms:
156° + m<3 = 180°
Same to both sides:
m<3 = 24°
Second way:
Exterior angle theorem.
118° = m<2 + m<3 + 49°
Plug in known-values:
118° = 45° + m<3 +49°
Combine like terms:
118° = 94° + m<3
Same to both sides:
24° = m<3
So m<3 = 24°
There you go! You just need to take it step-by-step and you can get the answer. Be open-minded, don't just try to go for a certain angle, see what you can do, and work from there. It all comes together at the end.
Let me know if you have any questions, have a good day!