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Which angle is supplementary to angle DCF

To determine which angle is supplementary to angle \( \angle DCF \), we need to understand the definition of supplementary angles. Supplementary angles are two angles whose measures add up to \(180^\circ\).

In the provided diagram:
- Point \(C\) is the intersection of the horizontal and vertical axes.
- Points \(A\) and \(E\) lie on the vertical axis.
- Points \(B\) and \(D\) lie on the horizontal axis.
- Point \(F\) is connected to \(C\) forming the angle \( \angle DCF \).

Angle \( \angle DCF \) is formed by the lines \( CD \) and \( CF \). The angle supplementary to \( \angle DCF \) must be the angle that, when added to \( \angle DCF \), equals \( 180^\circ \).

Observing the diagram, \( \angle DCB \) is a straight line, and it is a \(180^\circ\) angle. Since \( \angle DCF \) is part of \( \angle DCB \), the angle supplementary to \( \angle DCF \) is the angle on the opposite side of the line \( CD \).

Thus, the angle supplementary to \( \angle DCF \) is \( \angle BCF \).

Would you like more details on how supplementary angles work or have any other questions?

Here are 5 more questions you might find interesting:
1. What are complementary angles?
2. How do you find the measure of an unknown angle in a triangle?
3. What are vertically opposite angles?
4. How do you calculate the exterior angles of a polygon?
5. Can you explain the properties of parallel lines and transversal angles?

**Tip:** When dealing with angles, always remember that the sum of angles around a point is \(360^\circ\) and the sum of angles on a straight line is \(180^\circ\).

Explore the concept of supplementary angles with a focus on angle DCF. Learn how to identify angles that sum up to 180 degrees, using diagrams and detailed explanations. Suitable for Grades 6-8 students.

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