Question

Select the correct answer from each drop-down menu. a student is given ∠ qos ≅ ∠ rot and the diagram and asked to prove m ∠ qor = 56 ∘ . given: ∠ qos ≅ ∠ rot prove: m ∠ qor = 56 ∘ two lines or and os intersect at o. another line qt passes through the point o, which makes the angle 56 degrees on sot. here is the student's proof. given 1. angle qos congruent angle tor pointing, 2. m angle qos equals m angle rot pointing, 3. m angle qor plus m angle ros equals m angle tos plus m angle ros pointing, 4. m angle qor equals m angle tos pointing, 5. m angle tos equals 56

Answer 1

The goal is to prove that ∠ QOR = 56°, which we cannot do with the given statements as they lead to a contradiction. Instead, they suggest that ∠ QOR = 124°, hence the proof must be revisited.

Step-by-step explanation:

The student is given ∠ QOS ≅ ∠ ROT and must prove that the measure of ∠ QOR equals 56°. By the Angle Addition Postulate, since two angles ∠ QOS and ∠ SOT form a straight line at point O, the measure of ∠ QOT (straight angle) is 180°. Hence, ∠ QOR + ∠ ROT = ∠ QOT which means ∠ QOR + ∠ QOS = 180°.

We know ∠ QOS is congruent to ∠ ROT, therefore, their measures are equal. Replacing this into the equation gives us ∠ QOR + ∠ QOR = 180°, or 2 × ∠ QOR = 180°, so ∠ QOR = 90°. But we're also given that ∠ QOR + ∠ SOT = 180° and ∠ SOT = 56°, so ∠ QOR = 180° - 56°, which results in ∠ QOR = 124°.

This calculation contains a contradiction; thus, the provided proof in the information is incorrect or incomplete.