which set of three angles could represent the interior angles of a triangle?

$19^{\circ}, 70^{\circ}, 91^{\circ}$
$47^{\circ}, 12^{\circ}, 31^{\circ}$
$50^{\circ}, 20^{\circ}, 20^{\circ}$
$25^{\circ}, 25^{\circ}, 100^{\circ}$

Question

which set of three angles could represent the interior angles of a triangle?

$19^{\circ}, 70^{\circ}, 91^{\circ}$
$47^{\circ}, 12^{\circ}, 31^{\circ}$
$50^{\circ}, 20^{\circ}, 20^{\circ}$
$25^{\circ}, 25^{\circ}, 100^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem" ] } ## State the relevant geometric theorem $$ \text{Sum of interior angles of a triangle} = 180^\circ $$ ## Calculate the sum for each option $$ \begin{aligned} &19^\circ + 70^\circ + 91^\circ = 180^\circ \ &47^\circ + 12^\circ + 31^\circ = 90^\circ \ &50^\circ + 20^\circ + 20^\circ = 90^\circ \ &25^\circ + 25^\circ + 100^\circ = 150^\circ \end{aligned} $$ ## Identify the correct set $$ 19^\circ + 70^\circ + 91^\circ = 180^\circ $$

(A) $19^\circ, 70^\circ, 91^\circ$

(B) $47^\circ, 12^\circ, 31^\circ$

(C) $50^\circ, 20^\circ, 20^\circ$

(D) $25^\circ, 25^\circ, 100^\circ$

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

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QUESTION IMAGE

Question

Explanation:

State the relevant geometric theorem

Calculate the sum for each option

Identify the correct set

Answer: