in the following figure, $\overline{eb}$ and $\overline{dc}$ intersect at point a.
what is the value of $x$ in the figure?
$x = $

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Triangle Congruence Criteria" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Triangle Congruence Criteria", "Vertical Angles", "Congruent Triangles Angle Correspondence" ] } ## Identify congruent parts in triangles ADE and ACB $$ \begin{aligned} &AE = AC = 3.8 \ &AD = AB = 4.6 \ &\angle DAE = \angle BAC = 37^\circ \quad \text{(vertical angles)} \end{aligned} $$ ## Prove triangle congruence $$ \triangle ADE \cong \triangle ABC \quad \text{(SAS Congruence)} $$ ## Solve for the unknown angle x $$ \begin{aligned} &\angle E = \angle C = 180^\circ - 37^\circ - 68^\circ = 75^\circ \ &x = \angle D = \angle B = 68^\circ \end{aligned} $$ What is the value of $x$ in the figure? $x =$ 68 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Criteria" ] }

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Question

Explanation:

Identify congruent parts in triangles ADE and ACB

Prove triangle congruence

Solve for the unknown angle x

Answer: