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

$x = \box$

Question

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

$x = \box$

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" ], "new_concepts": [ "Congruent Triangles Angle Correspondence" ], "current_concepts": [ "Triangle Congruence Criteria", "Triangle Angle Sum Theorem" ] } ## Prove triangle congruence $$ \begin{aligned} &AC = BD = 4.4 \ &AB = CD = 4 \ &BC = CB \quad \text{(Reflexive Property)} \ &\triangle ABC \cong \triangle DCB \quad \text{(SSS Congruence)} \end{aligned} $$ ## Find corresponding angles $$ \begin{aligned} &\angle ACB = \angle DBC = x^\circ \ &\angle ABC = \angle DCB = 61^\circ \ &\angle BAC = \angle CDB = 180^\circ - (52^\circ + 61^\circ) = 67^\circ \end{aligned} $$ ## Solve for x $$ \begin{aligned} &x^\circ = \angle ACB = 52^\circ \ &x = 52 \end{aligned} $$ What is the value of $x$ in the figure shown below? $x =$ 52 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Criteria" ] }

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Question

Explanation:

Prove triangle congruence

Find corresponding angles

Solve for x

Answer: