triangle $\delta abc$ is rotated $-120^\circ$ about point $p$ to create $\delta abc$.

what is the measure of $\angle a$?

Question

triangle $\delta abc$ is rotated $-120^\circ$ about point $p$ to create $\delta abc$.

what is the measure of $\angle a$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Transformations", "Rotations in Geometry" ], "new_concepts": [ "Rigid Transformations", "Triangle Angle Sum Theorem" ], "current_concepts": [ "Geometric Transformations", "Rotations in Geometry", "Rigid Transformations", "Triangle Angle Sum Theorem" ] } ## Identify corresponding angles under rotation $$ \begin{aligned} &\triangle ABC \cong \triangle A'B'C' \quad \text{(Rotations are rigid transformations)} \ &m\angle A' = m\angle A \ &m\angle B' = m\angle B \ &m\angle C' = m\angle C \end{aligned} $$ ## Determine the measure of the corresponding angle $$ \begin{aligned} &m\angle A = 40^\circ \ &m\angle A' = m\angle A = 40^\circ \end{aligned} $$ What is the measure of $\angle A'$? $40$$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Rotations in Geometry" ] }

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Explanation:

Identify corresponding angles under rotation

Determine the measure of the corresponding angle

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