triangle qrs has the angle measures shown.

$m\angle q = (1x)^\circ$
$m\angle r = (3x)^\circ$
$m\angle s = (6x)^\circ$

what is the measure of the obtuse angle?

18
54
108
216

Question

triangle qrs has the angle measures shown.

$m\angle q = (1x)^\circ$
$m\angle r = (3x)^\circ$
$m\angle s = (6x)^\circ$

what is the measure of the obtuse angle?

18
54
108
216

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", "Obtuse Triangle Definition" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Obtuse Triangle Definition" ] } ## Set up the angle sum equation Using the **Triangle Angle Sum Theorem** knowledge point $$ \begin{aligned} m\angle Q + m\angle R + m\angle S &= 180^\circ \ (1x)^\circ + (3x)^\circ + (6x)^\circ &= 180^\circ \end{aligned} $$ ## Solve for x Using the **Triangle Angle Sum Theorem** knowledge point $$ \begin{aligned} 10x &= 180 \ x &= 18 \end{aligned} $$ ## Calculate the angle measures Using the **Triangle Angle Sum Theorem** knowledge point $$ \begin{aligned} m\angle Q &= 1(18)^\circ = 18^\circ \ m\angle R &= 3(18)^\circ = 54^\circ \ m\angle S &= 6(18)^\circ = 108^\circ \end{aligned} $$ ## Identify the obtuse angle Using the **Obtuse Triangle Definition** knowledge point $$ \begin{aligned} &108^\circ > 90^\circ \ &\text{Obtuse angle} = 108^\circ \end{aligned} $$

18

54

108

216

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Angle Sum Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the angle sum equation

Solve for x

Calculate the angle measures

Identify the obtuse angle

Answer: