Question

given the intersecting segments
given ∠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 substitution property of equality, m∠boc = 90°.
which statement is measuring true?
a. ∠aob and ∠boc are vertical angles
b. ∠aob and ∠boc form a linear pair
c. ∠cod and ∠aod form a linear pair
d. ∠doa and ∠boc are a vertical angles

Explanation:

Step1: Recall vertical angles

Vertical angles are equal. If two angles are vertical angles, their measures are the same.

Step2: Analyze each option

• Option A: ∠AOB and ∠DOC are vertical angles. By the vertical - angles theorem, \(m\angle AOB=m\angle DOC\).
• Option B: ∠AOB and ∠BOC form a linear pair. A linear pair of angles is supplementary (\(m\angle AOB + m\angle BOC=180^{\circ}\)), not equal.
• Option C: ∠COD and ∠AOD form a linear pair. A linear pair of angles is supplementary (\(m\angle COD + m\angle AOD = 180^{\circ}\)), not equal.
• Option D: ∠DOA and ∠BOC. There is no property (such as vertical - angles or congruent - angles due to parallel lines etc.) that makes them equal in measure.

Answer:

A. ∠AOB and ∠DOC are vertical angles