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If m 21 = 40°, find m 2. %3D 3. O 140° О 60° O 40° О.50°

If m 21 = 40°, find m 2. %3D 3. O 140° О 60° O 40° О.50°

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Question: If \( m \angle 1 = 40^\circ \), find \( m \angle 2 \). ### Diagram: The diagram displays two intersecting lines forming four angles labeled as 1, 2, 3, and 4. ### Answer Choices: - \( \circ \) 140° - \( \circ \) 60° - \( \circ \) 40° - \( \circ \) 50° ### Explanation of Diagram: The intersecting lines create vertical angles. Vertical angles are congruent, meaning they have the same measure. In the diagram: - \( \angle 1 \) and \( \angle 3 \) are vertical angles. - \( \angle 2 \) and \( \angle 4 \) are vertical angles. Thus, \( m \angle 1 = m \angle 3 \) and \( m \angle 2 = m \angle 4 \). ### Solution: Given \( m \angle 1 = 40^\circ \), we find \( m \angle 2 \) using the properties of vertical angles and the fact that angles on a straight line sum up to \( 180^\circ \). Therefore: - \( \angle 1 + \angle 2 = 180^\circ \) - \( 40^\circ + m \angle 2 = 180^\circ \) - \( m \angle 2 = 180^\circ - 40^\circ = 140^\circ \) ### Correct Answer: - \( \circ \) 140°
Transcribed Image Text:### Question: If \( m \angle 1 = 40^\circ \), find \( m \angle 2 \). ### Diagram: The diagram displays two intersecting lines forming four angles labeled as 1, 2, 3, and 4. ### Answer Choices: - \( \circ \) 140° - \( \circ \) 60° - \( \circ \) 40° - \( \circ \) 50° ### Explanation of Diagram: The intersecting lines create vertical angles. Vertical angles are congruent, meaning they have the same measure. In the diagram: - \( \angle 1 \) and \( \angle 3 \) are vertical angles. - \( \angle 2 \) and \( \angle 4 \) are vertical angles. Thus, \( m \angle 1 = m \angle 3 \) and \( m \angle 2 = m \angle 4 \). ### Solution: Given \( m \angle 1 = 40^\circ \), we find \( m \angle 2 \) using the properties of vertical angles and the fact that angles on a straight line sum up to \( 180^\circ \). Therefore: - \( \angle 1 + \angle 2 = 180^\circ \) - \( 40^\circ + m \angle 2 = 180^\circ \) - \( m \angle 2 = 180^\circ - 40^\circ = 140^\circ \) ### Correct Answer: - \( \circ \) 140°
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