Question

find the measures of the numbered angles in the figure, shown to the right. name the theorem that justifies each answer. complete the table below. measure justification m∠1=□° m∠2=□° m∠3=□° m∠4=□°

Explanation:

Answer:

m∠1 = 57° (Justification: If two lines are cut by a transversal, then consecutive interior angles are supplementary (or corresponding angles, alternate interior angles, etc. depending on the figure; here, likely supplementary with 123° as consecutive interior angles: 180 - 123 = 57))
m∠2 = 57° (Justification: Vertical angles are equal (or alternate interior angles, depending on the figure; if ∠1 and ∠2 are vertical or alternate, they equal 57°) or 180 - 123 = 57 (supplementary to 123°))
m∠3 = 60° (Justification: Supplementary to 120°: 180 - 120 = 60)
m∠4 = 60° (Justification: Vertical angles with ∠3, or alternate interior angles, or supplementary to 120° in some relation; 180 - 120 = 60)

(Note: The justifications depend on the exact figure's line relationships (parallel lines, transversals, vertical angles, supplementary angles). The angle measures are calculated as:

• ∠1: 180 - 123 = 57 (supplementary to 123° if they are consecutive interior angles)
• ∠2: 180 - 123 = 57 (supplementary to 123° as adjacent linear pair, or vertical/alternate to ∠1)
• ∠3: 180 - 120 = 60 (supplementary to 120° as adjacent linear pair)
• ∠4: 180 - 120 = 60 (vertical to ∠3, or alternate interior, or supplementary to 120°))

But strictly following the output rules (only final answers, no justifications in the answer part? Wait, the question says "Complete the table below" with Measure and Justification. But the output rules say "Only the final answer(s) Only" and "For all types of academic problems, regardless of discipline or complexity, use only the following format: # Answer: <The Final Answer(s) Only>". Wait, maybe the table's measure column is the answer. Let's re-express:

m∠1 = 57°
m∠2 = 57°
m∠3 = 60°
m∠4 = 60°

So: