Question

which angles are supplementary to each other? select all that apply.
$\angle ecf$ and $\angle dea$
$\angle ecf$ and $\angle bec$
$\angle aeb$ and $\angle dea$
$\angle gch$ and $\angle aeb$

Explanation:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

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

$\angle ECF$ and $\angle DEA$ are congruent (corresponding angles), not supplementary.

Step3: Analyze $\angle ECF$ and $\angle BEC$

$\angle ECF$ and $\angle BEC$ are same-side interior angles, so they sum to $180^\circ$.

Step4: Analyze $\angle AEB$ and $\angle DEA$

$\angle AEB$ and $\angle DEA$ form a linear pair, so they sum to $180^\circ$.

Step5: Analyze $\angle GCH$ and $\angle AEB$

$\angle GCH \cong \angle ECF$ (vertical angles), and $\angle ECF \cong \angle DEA$ (corresponding angles). $\angle AEB + \angle DEA = 180^\circ$, so $\angle GCH + \angle AEB = 180^\circ$.

Answer:

• $\angle ECF$ and $\angle BEC$
• $\angle AEB$ and $\angle DEA$
• $\angle GCH$ and $\angle AEB$