in the diagram, $m\angle acb = 65$.
find $m\angle bcd$.

$m\angle bcd = \square^{\circ}$.

Question

in the diagram, $m\angle acb = 65$.
find $m\angle bcd$.

$m\angle bcd = \square^{\circ}$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Complementary Angles", "Perpendicular Lines" ], "current_concepts": [ "Complementary Angles", "Perpendicular Lines", "Angle Addition Postulate" ] } ## Identify the geometric relationships from the diagram $$ \begin{aligned} &\text{Line } EB \text{ is a straight line intersecting line } FD \text{ at point } C.\ &AC \perp FD \implies m\angle ACD = 90^\circ\ &m\angle ACD = m\angle ACB + m\angle BCD \end{aligned} $$ ## Substitute the given value and solve for the unknown angle $$ \begin{aligned} &65^\circ + m\angle BCD = 90^\circ\ &m\angle BCD = 90^\circ - 65^\circ\ &m\angle BCD = 25^\circ \end{aligned} $$ In the diagram, $m\angle ACB = 65$. Find $m\angle BCD$. $m\angle BCD =$ 25$^\circ$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Complementary Angles" ] }

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Question

Explanation:

Identify the geometric relationships from the diagram

Substitute the given value and solve for the unknown angle

Answer: