Thank you for the clearer image! Let’s analyze the given problem step by step.

The problem states that $BD$ and $EG$ are parallel lines, and you are tasked with finding $m\angle EFC$ given that $m\angle DCF = 110^\circ$.

Solution:

Step 1: Recognize the relationship between the angles

From the diagram:

• $\angle DCF$ and $\angle EFC$ are supplementary because they are adjacent angles forming a straight line (linear pair).

Step 2: Apply the supplementary angle rule

Angles forming a straight line always add up to $180^\circ$. Thus: $m\angle DCF + m\angle EFC = 180^\circ$

Step 3: Solve for $m\angle EFC$

$110^\circ + m\angle EFC = 180^\circ$ $m\angle EFC = 180^\circ - 110^\circ$ $m\angle EFC = 70^\circ$

Final Answer:

$m\angle EFC = 70^\circ$

Would you like an explanation of parallel line angle properties or any additional help?

Related Questions:

1. How do we use alternate interior angles to identify relationships in parallel lines?
2. What is the significance of corresponding angles in this setup?
3. If $m\angle DCF = 110^\circ$, what is $m\angle HFE$ in the diagram?
4. Can you identify another pair of supplementary angles in this figure?
5. What would happen to these relationships if the lines were not parallel?

Tip: When working with parallel lines and transversals, always look for alternate interior, corresponding, and supplementary angles to simplify the solution process!