Question

since ∠coa is complementary to ∠aof, m∠coa + m∠aof = 90°. since ∠eob forms a vertical angle with ∠aof, they are congruent by the vertical angle theorem. by the substitution property of equality, m∠coa + 40° = 90°. applying the subtraction property of equality gives m∠coa = 50°. what is missing from the proof? the proof did not explain why that implies could have used the angle bod is congruent to angle coa angle eob is congruent to angle coa angle eob is congruent to angle aof angle bod is congruent to angle aof

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. \(\angle EOB\) and \(\angle AOF\) are vertical angles.

Step2: Analyze the proof logic

The proof uses the fact that \(\angle COA\) and \(\angle AOF\) are complementary (\(m\angle COA + m\angle AOF=90^{\circ}\)), and then tries to relate another angle. Since \(\angle EOB\) and \(\angle AOF\) are vertical angles (so \(m\angle EOB = m\angle AOF\)), and the proof is about showing an angle - congruence relation.

Answer:

angle EOB is congruent to angle AOF