By taking into account the given image, if m∠A = 120°, then angle ∠1 is 60°.
This is becasue both angles ∠A and ∠1 form a striaght angle together. That is, they add up 180°:
m∠A + m∠1 = 180° solve for m∠1 and replace m∠A = 120°
m∠1 = 180 - m∠A
m∠1 = 180 - 120 = 60°
Hence, the measure of angle 1 is 60°
The sum of angles ∠1, ∠2 and ∠B must be equal to 180°. You know what is the measure of angle ∠B (80°) and angle ∠1 (60°). Then, you have:
m∠1 + m∠B + m∠2 = 180
solve for m∠2 and replace the measure of other angles:
m∠2 = 180 - m∠1 - m∠B
m∠2 = 180 - 60 - 80
m∠2 = 40°
Hence, the measure of angle 2 is 40°
To determine the measure of angle C, you consider that angle next to B, with angle B form a straight angle together. Then, they ad up 180°. Such unknow angle is equal to the difference between 180° and measure of angle B (80°). If the unknown angle is D, you have:
m∠D = 180° - m∠B
m∠D = 180 - 80 = 100°
Next, you consider that the sum of angles ∠C, ∠D and the angle of 49° is equal to 180°:
m∠C + m∠D + 49 = 180 solve for m∠C and replace m∠D = 100°
m∠C = 180 - 49 - m∠D
m∠C = 180 - 49 - 100
m∠C = 31°
Hence, the measure of angle C is 31°