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AABC is similar to ADEF. D A 21° B E Find the measure of each angle. (a) C (b) D (c) F

AABC is similar to ADEF. D A 21° B E Find the measure of each angle. (a) C (b) D (c) F

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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### Similar Triangles: Finding Angle Measures In the image above, you are provided with two similar triangles, △ABC and △DEF. Due to the properties of similarity, corresponding angles in similar triangles are congruent. ### Triangles and Angle Information 1. **Triangle △ABC**: - Angle A is given as 21°. - Angle B is shown as a right angle (90°). 2. **Triangle △DEF**: - Angle E is shown as a right angle (90°). Given the information, you need to find the measure of each angle. ### Calculations: - Since △ABC is similar to △DEF, the corresponding angles are the same: - Angle A corresponds to Angle D. - Angle B corresponds to Angle E. - Angle C corresponds to Angle F. - The sum of the interior angles in any triangle is always 180°. Using this property for △ABC: - Angle A + Angle B + Angle C = 180° - 21° + 90° + Angle C = 180° - Angle C = 180° - 111° = 69° Hence, each triangle has angles as follows: - Angle C = Angle F = 69° - Angle D = Angle A = 21° - Angle E = 90° (already given) ### Tasks Find the measure of each angle: (a) \( C = \) \_\_\_° **Answer:** 69° (b) \( D = \) \_\_\_° **Answer:** 21° (c) \( F = \) \_\_\_° **Answer:** 69° --- By understanding the properties of similar triangles and the sum of interior angles, you can determine the missing angle measures as shown.
Transcribed Image Text:### Similar Triangles: Finding Angle Measures In the image above, you are provided with two similar triangles, △ABC and △DEF. Due to the properties of similarity, corresponding angles in similar triangles are congruent. ### Triangles and Angle Information 1. **Triangle △ABC**: - Angle A is given as 21°. - Angle B is shown as a right angle (90°). 2. **Triangle △DEF**: - Angle E is shown as a right angle (90°). Given the information, you need to find the measure of each angle. ### Calculations: - Since △ABC is similar to △DEF, the corresponding angles are the same: - Angle A corresponds to Angle D. - Angle B corresponds to Angle E. - Angle C corresponds to Angle F. - The sum of the interior angles in any triangle is always 180°. Using this property for △ABC: - Angle A + Angle B + Angle C = 180° - 21° + 90° + Angle C = 180° - Angle C = 180° - 111° = 69° Hence, each triangle has angles as follows: - Angle C = Angle F = 69° - Angle D = Angle A = 21° - Angle E = 90° (already given) ### Tasks Find the measure of each angle: (a) \( C = \) \_\_\_° **Answer:** 69° (b) \( D = \) \_\_\_° **Answer:** 21° (c) \( F = \) \_\_\_° **Answer:** 69° --- By understanding the properties of similar triangles and the sum of interior angles, you can determine the missing angle measures as shown.
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