Question

question 2
name a set of complementary angles.
(image of angle diagram with points a, c, b on a horizontal line, e above c, d on a ray from c to upper right)
options:

• ∠ace and ∠acb
• ∠ecd and ∠dcb
• ∠ace and ∠ecb
• ∠acd and ∠dcb

Explanation:

Step1: Recall Complementary Angles Definition

Complementary angles sum to $90^\circ$.

Step2: Analyze the Diagram

• $\angle ACE$ is a right angle? No, $\angle ACE$ is $90^\circ$? Wait, $AC \perp EC$ (right angle at $C$), so $\angle ACE = 90^\circ$.
• For $\angle ECD$ and $\angle DCB$: $\angle ECB$ is a right angle? Wait, $AC$ and $CB$ are a straight line, $EC \perp AC$, so $\angle ECB = 90^\circ$. Thus, $\angle ECD + \angle DCB = \angle ECB = 90^\circ$, so they are complementary.
• Check other options:
• $\angle ACE$ and $\angle ACB$: $\angle ACB$ is a straight angle ($180^\circ$), sum $

eq 90^\circ$.

• $\angle ACE$ and $\angle ECB$: $\angle ACE = 90^\circ$, $\angle ECB = 90^\circ$, sum $= 180^\circ$ (supplementary).
• $\angle ACD$ and $\angle DCB$: $\angle ACD + \angle DCB = \angle ACB = 180^\circ$ (supplementary).

Thus, $\angle ECD$ and $\angle DCB$ are complementary.

Answer:

B. $\angle ECD$ and $\angle DCB$