19. abcd is a parallelogram and cde is a triangle. adf and bce are straight lines.
find $\angle fde$.

20. abcd is a square and aecf is a parallelogram. find $\angle fcd$.

Question

19. abcd is a parallelogram and cde is a triangle. adf and bce are straight lines.
find $\angle fde$.

20. abcd is a square and aecf is a parallelogram. find $\angle fcd$.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Parallel Line Angle Properties" ], "new_concepts": [ "Parallelogram Angle Properties", "Square Angle Properties" ], "current_concepts": [ "Parallel Line Angle Properties", "Parallelogram Angle Properties", "Square Angle Properties" ] } ## Question 19: Find angle ADC Using the *Parallel Line Angle Properties* knowledge point $$ \begin{aligned} &\angle ADC = \angle B = 63^\circ \end{aligned} $$ ## Question 19: Find angle FDE Using the *Parallel Line Angle Properties* knowledge point $$ \begin{aligned} &\angle FDE = \angle DEC = 48^\circ \end{aligned} $$ ## Question 20: Find angle EAD Since $ABCD$ is a square, $\angle BAD = 90^\circ$. $$ \begin{aligned} \angle EAD &= \angle BAD - \angle BAE \ &= 90^\circ - 79^\circ \ &= 11^\circ \end{aligned} $$ ## Question 20: Find angle FCD Since $AECF$ is a parallelogram, opposite sides $AE$ and $FC$ are parallel. Thus, the alternate interior angles are equal: $$ \begin{aligned} \angle FCD &= \angle EAD \ &= 11^\circ \end{aligned} $$ ## Question 19 $48^\circ$ ## Question 20 $11^\circ$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Angle Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Question 19: Find angle ADC

Question 19: Find angle FDE

Question 20: Find angle EAD

Question 20: Find angle FCD

Answer:

Question 19

Question 20