in a right triangle, one unknown angle is twice as large as the other unknown angle. determine the measure of the missing angles.

$30^\circ$ and $90^\circ$
$30^\circ$ and $60^\circ$
$90^\circ$ and $60^\circ$
$40^\circ$ and $20^\circ$

Question

in a right triangle, one unknown angle is twice as large as the other unknown angle. determine the measure of the missing angles.

$30^\circ$ and $90^\circ$
$30^\circ$ and $60^\circ$
$90^\circ$ and $60^\circ$
$40^\circ$ and $20^\circ$

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", "Complementary Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Complementary Angles" ] } ## Set up the equation for the unknown angles $$ \begin{aligned} &\text{Let the smaller unknown angle be } x.\ &\text{The other unknown angle is } 2x.\ &x + 2x = 90^\circ \end{aligned} $$ ## Solve for the unknown angles $$ \begin{aligned} &3x = 90^\circ\ &x = 30^\circ\ &2x = 60^\circ \end{aligned} $$

(A) $30^\circ$ and $90^\circ$

(B) $30^\circ$ and $60^\circ$

(C) $90^\circ$ and $60^\circ$

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

{ "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 equation for the unknown angles

Solve for the unknown angles

Answer: