triangle abc has the angle measures shown.

$m\angle a = (2x)^\circ$
$m\angle b = (3x)^\circ$
$m\angle c = (4x)^\circ$

which statement is true about the angles?

$m\angle a = 20^\circ$
$m\angle b = 60^\circ$
$\angle a$ and $\angle b$ are complementary
$m\angle a + m\angle c = 100^\circ$

Question

triangle abc has the angle measures shown.

$m\angle a = (2x)^\circ$
$m\angle b = (3x)^\circ$
$m\angle c = (4x)^\circ$

which statement is true about the angles?

$m\angle a = 20^\circ$
$m\angle b = 60^\circ$
$\angle a$ and $\angle b$ are complementary
$m\angle a + m\angle c = 100^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Geometry", "Complementary Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Geometry", "Complementary Angles", "Angle Measures" ] } ## Sum the interior angles of the triangle $$ (2x)^\circ + (3x)^\circ + (4x)^\circ = 180^\circ $$ $$ 9x = 180 \implies x = 20 $$ ## Calculate each individual angle measure $$ \begin{aligned} m\angle A &= 2(20)^\circ = 40^\circ \ m\angle B &= 3(20)^\circ = 60^\circ \ m\angle C &= 4(20)^\circ = 80^\circ \end{aligned} $$ ## Evaluate the given statements $$ \begin{aligned} &m\angle A = 20^\circ \quad (\text{False, since } m\angle A = 40^\circ) \ &m\angle B = 60^\circ \quad (\text{True}) \ &\angle A \text{ and } \angle B \text{ are complementary} \quad (40^\circ + 60^\circ = 100^\circ e 90^\circ, \text{ False}) \ &m\angle A + m\angle C = 100^\circ \quad (40^\circ + 80^\circ = 120^\circ e 100^\circ, \text{ False}) \end{aligned} $$

(A) $m\angle A = 20^\circ$

(B) $m\angle B = 60^\circ$

(C) $\angle A$ and $\angle B$ are complementary

(D) $m\angle A + m\angle C = 100^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Sum the interior angles of the triangle

Calculate each individual angle measure

Evaluate the given statements

Answer: