Question

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 doa ) and ( angle boc ) are vertical angles.
b. ( angle cod ) and ( angle aod ) form a linear pair.
c. ( angle aob ) and ( angle boc ) form a linear pair.
d. ( angle aob ) and ( angle doc ) are vertical angles.

Explanation:

• A linear pair of angles is formed when two adjacent angles are supplementary (sum to \(180^{\circ}\)).
• In the proof, it is stated that \(\angle AOB\) is supplementary to \(\angle BOC\). For two angles to be supplementary in this context (using the property of a linear - pair sum), they must form a linear pair.
• Option C: \(\angle AOB\) and \(\angle BOC\) form a linear pair. This is the missing statement. If two angles form a linear pair, then the sum of their measures is \(180^{\circ}\) (by the linear - pair postulate).

Answer:

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