given parallelogram $abcd$, which of the following statements about its angles must be correct?

it has two pairs of complementary angles.
it has two pairs of supplementary angles.
all of its angles are acute.
the sum of the measures of its angles is $180^\circ$.

Question

given parallelogram $abcd$, which of the following statements about its angles must be correct?

it has two pairs of complementary angles.
it has two pairs of supplementary angles.
all of its angles are acute.
the sum of the measures of its angles is $180^\circ$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallelogram Properties" ], "new_concepts": [ "Consecutive Angles of Parallelogram" ], "current_concepts": [ "Parallelogram Properties", "Consecutive Angles of Parallelogram" ] } ## Analyze consecutive interior angles of a parallelogram $$ \begin{aligned} &m\angle A + m\angle B = 180^\circ \ &m\angle B + m\angle C = 180^\circ \ &m\angle C + m\angle D = 180^\circ \ &m\angle D + m\angle A = 180^\circ \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &\text{Complementary pairs: } \text{False (sum is } 180^\circ\text{, not } 90^\circ\text{)} \ &\text{Supplementary pairs: } \text{True (consecutive angles are supplementary)} \ &\text{All acute: } \text{False (at least two must be obtuse or right)} \ &\text{Sum of angles: } 360^\circ e 180^\circ \end{aligned} $$

It has two pairs of complementary angles.

It has two pairs of supplementary angles.

All of its angles are acute.

The sum of the measures of its angles is 180°.

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

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QUESTION IMAGE

Question

Explanation:

Analyze consecutive interior angles of a parallelogram

Evaluate the given options

Answer: