given that $\triangle abc \cong \triangle def$, determine the value of $x$ in the following diagram:

$x = 60$
$x = 5$
$x = 12$
$x = 250$

Question

given that $\triangle abc \cong \triangle def$, determine the value of $x$ in the following diagram:

$x = 60$
$x = 5$
$x = 12$
$x = 250$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Triangle Congruence Correspondence" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Triangle Congruence Correspondence" ] } ## Find the measure of angle B Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} m\angle B &= 180^\circ - (m\angle A + m\angle C) \ m\angle B &= 180^\circ - (65^\circ + 55^\circ) \ m\angle B &= 60^\circ \end{aligned} $$ ## Relate corresponding angles of congruent triangles Using the *Triangle Congruence Correspondence* knowledge point $$ \begin{aligned} \Delta ABC &\cong \Delta DEF \ \angle E &\cong \angle B \ m\angle E &= m\angle B = 60^\circ \end{aligned} $$ ## Solve for x Using the *Triangle Congruence Correspondence* knowledge point $$ \begin{aligned} 5x &= 60 \ x &= 12 \end{aligned} $$

(A) $x = 60$

(B) $x = 5$

(C) $x = 12$

(D) $x = 250$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Correspondence" ] }

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QUESTION IMAGE

Question

Explanation:

Find the measure of angle B

Relate corresponding angles of congruent triangles

Solve for x

Answer: