Question

in the figure shown, which pair of angles must be complementary?
○ ∠cob and∠aoc
○ ∠cod and ∠dob
○ ∠aoc and ∠dob
○ ∠aoc and∠cod

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Identify right angle

From the figure, $\angle COB = 90^\circ$, so $\angle COD + \angle DOB = 90^\circ$.

Step3: Analyze other pairs

• $\angle COB + \angle AOC$: $\angle COB=90^\circ$, sum exceeds $90^\circ$.
• $\angle AOC + \angle DOB$: No guarantee their sum is $90^\circ$.
• $\angle AOC + \angle COD$: Sum equals $\angle AOD$, not necessarily $90^\circ$.

Answer:

$\angle COD$ and $\angle DOB$