Question

which set of angles are complementary in this diagram?
options:
∠ecf and ∠acf
∠ecf and ∠bcf
∠dcf and ∠bcf
∠ecf and ∠dce

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Analyze $\angle ECF$ and $\angle BCF$

$\angle ACB = 90^\circ$, so $\angle ECB = 90^\circ$.
$\angle ECB = \angle ECF + \angle BCF$, so $\angle ECF + \angle BCF = 90^\circ$.

Step3: Verify other options

• $\angle ECF + \angle ACF > 90^\circ$ (forms obtuse angle)
• $\angle DCF + \angle BCF = 180^\circ$ (straight angle)
• $\angle ECF + \angle DCE > 90^\circ$ (forms obtuse angle)

Answer:

$\boldsymbol{\angle ECF \text{ and } \angle BCF}$