given that the following triangles are congruent, determine the value of $x$.

$x = 1$
$x = 396$
$x = 11$
$x = \frac{28}{3}$

Question

given that the following triangles are congruent, determine the value of $x$.

$x = 1$
$x = 396$
$x = 11$
$x = \frac{28}{3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence", "Corresponding Parts" ], "new_concepts": [], "current_concepts": [ "Triangle Congruence", "Corresponding Parts", "Triangle Angle Sum Theorem" ] } ## Identify corresponding parts of the congruent triangles $$ \begin{aligned} &\text{Side with single tick mark corresponds to side with single tick mark.}\ &\text{Side with double tick marks corresponds to side with double tick marks.}\ &\text{Side with triple tick marks corresponds to side with triple tick marks.}\ &\text{The angle } (6x - 6)^\circ \text{ is between the single-tick side and triple-tick side.}\ &\text{The corresponding angle in the right triangle is } 60^\circ. \end{aligned} $$ ## Set up the equation for x $$ 6x - 6 = 60 $$ ## Solve for x $$ \begin{aligned} &6x = 66\ &x = 11 \end{aligned} $$

$x = 1$

$x = 396$

$x = 11$

$x = \frac{28}{3}$

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

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QUESTION IMAGE

Question

Explanation:

Identify corresponding parts of the congruent triangles

Set up the equation for x

Solve for x

Answer: