Question

1.3.3 quiz: mathematical proofs: mastery test
given: ∠aob is a right angle
prove: m ∠ boc = 90°
since ∠aob is a right angle, it is 90°. ∠aob is supplementary to ∠boc,
so m ∠ aob + m ∠ boc = 180°. by the substitution property of equality,
90° + m ∠boc = 180°. applying the subtraction property of equality,
m ∠ boc = 90°.
what statement is missing from the proof?
a. ∠cod and ∠aod form a linear pair.
b. ∠doa and ∠boc are vertical angles.
c. ∠aob and ∠doc are vertical angles.
d. ∠aob and ∠boc form a linear pair

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles sum to \( 180^{\circ} \).

Step2: Recall the property of a linear pair

A linear pair of angles is supplementary.
Since \( \angle AOB\) and \( \angle BOC\) are supplementary ( \(m\angle AOB + m\angle BOC=180^{\circ}\)), they must form a linear pair. This is the missing statement in the proof.

Answer:

D. \( \angle AOB \) and \( \angle BOC \) form a linear pair.