in an obtuse isosceles triangle, one angle is $120^{\circ}$. determine the measure of the other two angles.

$30^{\circ}$ and $30^{\circ}$
$20^{\circ}$ and $40^{\circ}$
$20^{\circ}$ and $20^{\circ}$
$30^{\circ}$ and $40^{\circ}$

Question

in an obtuse isosceles triangle, one angle is $120^{\circ}$. determine the measure of the other two angles.

$30^{\circ}$ and $30^{\circ}$
$20^{\circ}$ and $40^{\circ}$
$20^{\circ}$ and $20^{\circ}$
$30^{\circ}$ and $40^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Classification", "Triangle Angle Sum Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Classification", "Triangle Angle Sum Theorem", "Isosceles Triangle Properties" ] } ## Identify properties of the triangle $$ \begin{aligned} &\text{Type: Obtuse isosceles triangle}\ &\text{Given angle: } 120^\circ \quad (\text{must be the unique obtuse vertex angle})\ &\text{Base angles: } x, \quad x \quad (\text{equal by isosceles properties}) \end{aligned} $$ ## Apply the angle sum theorem $$ \begin{aligned} &120^\circ + x + x = 180^\circ\ &2x = 60^\circ\ &x = 30^\circ \end{aligned} $$ ## Determine the other two angles $$ \text{Other two angles: } 30^\circ \text{ and } 30^\circ $$

(A) $30^\circ$ and $30^\circ$

(B) $20^\circ$ and $40^\circ$

(C) $20^\circ$ and $20^\circ$

(D) $30^\circ$ and $40^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify properties of the triangle

Apply the angle sum theorem

Determine the other two angles

Answer: