In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct? Check all that apply.
The choices are not provided, but we can determine which angle measures are correct based on the given information.
Since m∠3 = 120° and m∠12 = 80°, we can determine the measures of some other angles in the diagram.
Since ∠1, ∠2, ∠3, and ∠12 are all adjacent angles, their sum should be 360° (according to the angle addition postulate).
m∠1 + m∠2 + m∠3 + m∠12 = 360°
Therefore, m∠1 + m∠2 + 120° + 80° = 360°
m∠1 + m∠2 = 360° - 120° - 80° = 160°
So, the sum of ∠1 and ∠2 is 160°.
Since ∠1 and ∠2 are supplementary angles (forming a straight line), their sum should be 180°.
∠1 + ∠2 = 180°
Since m∠1 + m∠2 = 160°, it means that ∠1 and ∠2 do not form a straight line. Therefore, m∠1 + m∠2 = 160° is incorrect.
So, none of the angle measures are correct.