the two parallel lines are cut by the transversal shown. determine the measures of $\measuredangle 1$ through $\measuredangle 7$.

$m\measuredangle 1 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 2 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 3 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 4 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 5 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 6 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 7 = \square^{\circ}$ (simplify your answer.)

Question

the two parallel lines are cut by the transversal shown. determine the measures of $\measuredangle 1$ through $\measuredangle 7$.

$m\measuredangle 1 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 2 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 3 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 4 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 5 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 6 = \square^{\circ}$ (simplify your answer.)
$m\measuredangle 7 = \square^{\circ}$ (simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 7, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Parallel Lines", "Transversal Angles", "Angle Relationships" ], "current_concepts": [ "Parallel Lines", "Transversal Angles", "Angle Relationships" ] } ## Identify angle relationships with the given angle $$ \begin{aligned} &\text{Given angle} = 36^\circ\ &m\angle 1 = 180^\circ - 36^\circ = 144^\circ \quad \text{(Supplementary angles)}\ &m\angle 2 = 36^\circ \quad \text{(Vertical angles)}\ &m\angle 3 = m\angle 1 = 144^\circ \quad \text{(Vertical angles)} \end{aligned} $$ ## Determine measures of angles at the second intersection $$ \begin{aligned} &m\angle 4 = 36^\circ \quad \text{(Alternate interior angles)}\ &m\angle 5 = m\angle 1 = 144^\circ \quad \text{(Corresponding angles)}\ &m\angle 6 = m\angle 2 = 36^\circ \quad \text{(Corresponding angles)}\ &m\angle 7 = m\angle 3 = 144^\circ \quad \text{(Corresponding angles)} \end{aligned} $$ | No. | Answer | |---|---| | 1 | $144^\circ$ | | 2 | $36^\circ$ | | 3 | $144^\circ$ | | 4 | $36^\circ$ | | 5 | $144^\circ$ | | 6 | $36^\circ$ | | 7 | $144^\circ$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines and Transversals" ] }

No.	Answer
2	\(36^\circ\)
3	\(144^\circ\)
4	\(36^\circ\)
5	\(144^\circ\)
6	\(36^\circ\)
7	\(144^\circ\)

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QUESTION IMAGE

Question

Explanation:

Identify angle relationships with the given angle

Determine measures of angles at the second intersection

Answer: