Question

select the correct answer. given ∠aob is a right angle prove ( mangle boc = 90^circ ) since ( angle aob ) is a right angle, it is ( 90^circ ). ( angle aob ) is supplementary to ( angle boc ), so ( mangle aob + mangle boc = 180^circ ). by the substitution property of equality, ( 90^circ + mangle boc = 180^circ ). applying the subtraction property of equality, ( mangle boc = 90^circ ). what statement is missing from the proof? a. ( angle aob ) and ( angle boc ) form a linear pair. b. ( angle doa ) and ( angle boc ) are vertical angles. c. ( angle cod ) and ( angle aod ) form a linear pair. d. ( angle aob ) and ( angle doc ) are vertical angles.

Explanation:

To determine the missing statement, we analyze the proof. The proof uses the fact that \( \angle AOB \) and \( \angle BOC \) are supplementary (sum to \( 180^\circ \)). Supplementary angles that form a linear pair are adjacent and form a straight line. Option A states \( \angle AOB \) and \( \angle BOC \) form a linear pair, which is necessary to conclude they are supplementary (since linear pairs are supplementary). Option B is about vertical angles, which don't imply supplementary here. Option C is about a different pair of angles. Option D is about vertical angles, not relevant to \( \angle AOB \) and \( \angle BOC \)'s relationship. So the missing statement is that \( \angle AOB \) and \( \angle BOC \) form a linear pair.

Answer:

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