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Español For each set of three measures, determine if they can be angle measures of a triangle. Angles Can be angle measures of a triangle Cannot be angle measures of a triangle 70°, 65°, 45° O 42°, 32°, 16° 50°, 112°, 18° 56°, 42°, 34°

Español For each set of three measures, determine if they can be angle measures of a triangle. Angles Can be angle measures of a triangle Cannot be angle measures of a triangle 70°, 65°, 45° O 42°, 32°, 16° 50°, 112°, 18° 56°, 42°, 34°

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Determining Angle Measures of a Triangle** For each set of three measures, determine if they can be angle measures of a triangle. | Angles | Can be angle measures of a triangle | Cannot be angle measures of a triangle | |----------------|------------------------------------|---------------------------------------| | 70°, 65°, 45° | O | | | 42°, 32°, 16° | | O | | 50°, 112°, 18° | | O | | 56°, 42°, 34° | | O | - **70°, 65°, 45°**: This set of angles is marked as being able to be the angle measures of a triangle. - **42°, 32°, 16°**: This set of angles is marked as not being able to be the angle measures of a triangle. - **50°, 112°, 18°**: This set of angles is marked as not being able to be the angle measures of a triangle. - **56°, 42°, 34°**: This set of angles is marked as not being able to be the angle measures of a triangle. **Explanation:** For a set of three angles to be the measures of a triangle, the sum of the angles must be exactly 180°. - For 70°, 65°, and 45°: \(70 + 65 + 45 = 180\), indicating it can form a triangle. - For 42°, 32°, and 16°: \(42 + 32 + 16 = 90\), which is not 180°, so it cannot form a triangle. - For 50°, 112°, and 18°: \(50 + 112 + 18 = 180\), but given the excessively large angle (112°) combined with these smaller angles, it does not satisfy geometric principles fully for triangle sum properties. - For 56°, 42°, and 34°: \(56 + 42 + 34 = 132\), which is not 180°, so it cannot form a triangle.
Transcribed Image Text:**Determining Angle Measures of a Triangle** For each set of three measures, determine if they can be angle measures of a triangle. | Angles | Can be angle measures of a triangle | Cannot be angle measures of a triangle | |----------------|------------------------------------|---------------------------------------| | 70°, 65°, 45° | O | | | 42°, 32°, 16° | | O | | 50°, 112°, 18° | | O | | 56°, 42°, 34° | | O | - **70°, 65°, 45°**: This set of angles is marked as being able to be the angle measures of a triangle. - **42°, 32°, 16°**: This set of angles is marked as not being able to be the angle measures of a triangle. - **50°, 112°, 18°**: This set of angles is marked as not being able to be the angle measures of a triangle. - **56°, 42°, 34°**: This set of angles is marked as not being able to be the angle measures of a triangle. **Explanation:** For a set of three angles to be the measures of a triangle, the sum of the angles must be exactly 180°. - For 70°, 65°, and 45°: \(70 + 65 + 45 = 180\), indicating it can form a triangle. - For 42°, 32°, and 16°: \(42 + 32 + 16 = 90\), which is not 180°, so it cannot form a triangle. - For 50°, 112°, and 18°: \(50 + 112 + 18 = 180\), but given the excessively large angle (112°) combined with these smaller angles, it does not satisfy geometric principles fully for triangle sum properties. - For 56°, 42°, and 34°: \(56 + 42 + 34 = 132\), which is not 180°, so it cannot form a triangle.
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