what is an angle that is supplementary to $\angle dfe$?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Supplementary Angles", "Linear Pair" ], "new_concepts": [], "current_concepts": [ "Supplementary Angles", "Linear Pair", "Naming Angles" ] } ## Identify the given angle and lines Using the *Naming Angles* knowledge point The given angle is $\angle DFE$. The vertex is $F$. The rays forming this angle are $\vec{FD}$ and $\vec{FE}$. From the diagram, points $B$, $F$, and $D$ lie on a straight line, meaning $\vec{FB}$ and $\vec{FD}$ are opposite rays. Similarly, points $C$, $F$, and $E$ lie on a straight line, meaning $\vec{FC}$ and $\vec{FE}$ are opposite rays. ## Find a supplementary angle using linear pairs Using the *Supplementary Angles* and *Linear Pair* knowledge points $$ \begin{aligned} &\text{Line } BD \text{ is intersected by ray } \vec{FE}.\ &\angle DFE \text{ and } \angle BFE \text{ form a linear pair along line } BD.\ &\angle DFE + \angle BFE = 180^\circ \end{aligned} $$ ## Find an alternative supplementary angle Using the *Supplementary Angles* and *Linear Pair* knowledge points $$ \begin{aligned} &\text{Line } CE \text{ is intersected by ray } \vec{FD}.\ &\angle DFE \text{ and } \angle DFC \text{ form a linear pair along line } CE.\ &\angle DFE + \angle DFC = 180^\circ \end{aligned} $$ What is an angle that is supplementary to $\angle DFE$? $\angle BFE$ (or $\angle DFC$) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Supplementary Angles" ] }

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Question

Explanation:

Identify the given angle and lines

Find a supplementary angle using linear pairs

Find an alternative supplementary angle

Answer: