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12) 73° 150° 160° 35° 35° 148°

12) 73° 150° 160° 35° 35° 148°

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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# Sum of Angles in Triangles ## Problem 11: The diagram shows a triangle with one angle labeled as 35° and another as 150°. Additionally, there are two other lines interacting externally with the triangle, where one of the angles is 35°. The task is to find the unknown angle (?) labeled in the diagram. ### Explanation: In any triangle, the sum of the interior angles is always equal to 180°. Given the two known angles, we can find the third angle by subtracting the sum of the known angles from 180°. ## Problem 12: The diagram depicts another triangle with one angle labeled as 73° and another external angle of 160°. An additional angle of 148° is given, which is not part of the triangle but helps in defining the unknown angle (?) within the triangle. ### Explanation: To find the unknown angle in the triangle, make use of the properties of supplementary angles (angles that sum to 180°) and the rule that the sum of angles in a triangle is always 180°. ### Detailed Steps: 1. Use the known angles to find any supplementary angles. 2. Utilize the rule that the sum of the angles in the triangle is 180° to determine the unknown angles. It's important to apply these geometric principles methodically in each problem to find the missing angles accurately.
Transcribed Image Text:# Sum of Angles in Triangles ## Problem 11: The diagram shows a triangle with one angle labeled as 35° and another as 150°. Additionally, there are two other lines interacting externally with the triangle, where one of the angles is 35°. The task is to find the unknown angle (?) labeled in the diagram. ### Explanation: In any triangle, the sum of the interior angles is always equal to 180°. Given the two known angles, we can find the third angle by subtracting the sum of the known angles from 180°. ## Problem 12: The diagram depicts another triangle with one angle labeled as 73° and another external angle of 160°. An additional angle of 148° is given, which is not part of the triangle but helps in defining the unknown angle (?) within the triangle. ### Explanation: To find the unknown angle in the triangle, make use of the properties of supplementary angles (angles that sum to 180°) and the rule that the sum of angles in a triangle is always 180°. ### Detailed Steps: 1. Use the known angles to find any supplementary angles. 2. Utilize the rule that the sum of the angles in the triangle is 180° to determine the unknown angles. It's important to apply these geometric principles methodically in each problem to find the missing angles accurately.
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