If m∠BCD = 60 and m∠DEC = 80, what is the measure of ∠DEF
not having a diagram to refer to, it's impossible to say. Provide some description of the relative positions of B,C,D,E,F.
I can think of various arrangements that provide different answers.
To find the measure of ∠DEF, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
First, let's draw a diagram to visualize the given information:
```
C
/ \
/ \
/ \
/ \
B───D───E
```
We know that m∠BCD is 60 degrees and m∠DEC is 80 degrees.
To find ∠DEF, we can start by finding ∠BDE. Since ∠BCD is 60 degrees, and ∠BCD and ∠BDE are vertical angles, we know that ∠BDE is also 60 degrees.
Next, we can find ∠ECD. Since ∠ECD and ∠DEC are corresponding angles, and ∠DEC is 80 degrees, we know that ∠ECD is also 80 degrees.
Now, we can find ∠CDE. Since ∠CDE is an exterior angle of ∆BDE, it is equal to the sum of the two remote interior angles, ∠BDE and ∠ECD. Therefore, ∠CDE = ∠BDE + ∠ECD = 60 degrees + 80 degrees = 140 degrees.
Finally, we can find ∠DEF. Since ∠DEF and ∠CDE are corresponding angles, and ∠CDE is 140 degrees, we know that ∠DEF is also 140 degrees.
Therefore, the measure of ∠DEF is 140 degrees.