what is the value of $x$ in the figure shown below?

$x = \square$

Question

what is the value of $x$ in the figure shown below?

$x = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence Criteria", "Triangle Angle Sum Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Congruence Criteria", "Triangle Angle Sum Theorem", "Congruent Triangles Angle Correspondence" ] } ## Prove triangle congruence $$ \begin{aligned} &AC = BD = 5.1 \ &AB = CD = 3.4 \ &BC = CB \quad \text{(Reflexive Property)} \ &\triangle ABC \cong \triangle DCB \quad \text{(SSS Congruence)} \end{aligned} $$ ## Find the missing angle in triangle ABC $$ \begin{aligned} &\angle ACB = 39^\circ \ &\angle ABC = 73^\circ \ &\angle BAC = 180^\circ - (39^\circ + 73^\circ) = 68^\circ \end{aligned} $$ ## Determine the value of x $$ \begin{aligned} &\angle BDC \text{ corresponds to } \angle CAB \ &x^\circ = \angle BDC = \angle CAB = 68^\circ \ &x = 68 \end{aligned} $$ What is the value of $x$ in the figure shown below? $x =$ 68 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Criteria" ] }

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QUESTION IMAGE

Question

Explanation:

Prove triangle congruence

Find the missing angle in triangle ABC

Determine the value of x

Answer: