The Exterior Angle Theorem states that in a triangle, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. For example, if a triangle has interior angles of 30 degrees and 70 degrees adjacent to the exterior angle, and the third interior angle is 80 degrees, then the exterior angle at that vertex would measure 30 + 70 = 100 degrees. This theorem is useful in solving problems involving triangles and their angles, as it provides a direct relationship between the exterior and interior angles.
Table of Contents
- Part 1: OnlineExamMaker AI Quiz Generator – Save Time and Efforts
- Part 2: 20 Exterior Angle Theorem Quiz Questions & Answers
- Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
Part 1: OnlineExamMaker AI Quiz Generator – Save Time and Efforts
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Part 2: 20 Exterior Angle Theorem Quiz Questions & Answers
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1. Question: In a triangle, if the interior angles are 30° and 40°, and the exterior angle at the third vertex is to be found, what is its measure?
A. 70°
B. 80°
C. 90°
D. 110°
Answer: A. 70°
Explanation: The exterior angle equals the sum of the two non-adjacent interior angles, so 30° + 40° = 70°.
2. Question: For a triangle with angles 50°, 60°, and 70°, what is the measure of the exterior angle at the 70° vertex?
A. 110°
B. 120°
C. 130°
D. 140°
Answer: A. 110°
Explanation: The exterior angle at the 70° vertex is 50° + 60° = 110°.
3. Question: If an exterior angle of a triangle measures 100° and one non-adjacent interior angle is 40°, what is the other non-adjacent interior angle?
A. 50°
B. 60°
C. 70°
D. 80°
Answer: B. 60°
Explanation: The exterior angle equals the sum of the two non-adjacent interior angles, so if one is 40°, the other is 100° – 40° = 60°.
4. Question: In a triangle, the interior angles are 25°, 65°, and 90°. What is the exterior angle at the 90° vertex?
A. 90°
B. 115°
C. 155°
D. 180°
Answer: A. 90°
Explanation: The exterior angle at the 90° vertex is 25° + 65° = 90°.
5. Question: An exterior angle of a triangle is 135°. If one non-adjacent interior angle is 55°, what is the measure of the other?
A. 70°
B. 80°
C. 90°
D. 100°
Answer: B. 80°
Explanation: The exterior angle is the sum of the two non-adjacent interior angles, so 135° – 55° = 80°.
6. Question: For a triangle with angles 40°, 70°, and 70°, the exterior angle at one of the 70° vertices is:
A. 110°
B. 120°
C. 140°
D. 150°
Answer: A. 110°
Explanation: The exterior angle at a 70° vertex is 40° + 70° = 110°.
7. Question: If the exterior angle at a vertex is 95° and the adjacent interior angle is 85°, what is the sum of the other two interior angles?
A. 10°
B. 95°
C. 180°
D. 95° (same as exterior)
Answer: B. 95°
Explanation: The exterior angle equals the sum of the two non-adjacent interior angles, which is 95°.
8. Question: In a triangle, angles are 30°, 100°, and 50°. The exterior angle at the 100° vertex is:
A. 80°
B. 130°
C. 150°
D. 180°
Answer: A. 80°
Explanation: The exterior angle at the 100° vertex is 30° + 50° = 80°.
9. Question: An exterior angle measures 160°. One non-adjacent interior angle is 70°. What is the other?
A. 90°
B. 100°
C. 110°
D. 120°
Answer: A. 90°
Explanation: The exterior angle is the sum, so 160° – 70° = 90°.
10. Question: For a triangle with angles 20°, 30°, and 130°, the exterior angle at the 130° vertex is:
A. 50°
B. 60°
C. 70°
D. 80°
Answer: A. 50°
Explanation: The exterior angle at the 130° vertex is 20° + 30° = 50°.
11. Question: If an exterior angle is 105° and one non-adjacent angle is 45°, the other non-adjacent angle is:
A. 50°
B. 60°
C. 70°
D. 80°
Answer: B. 60°
Explanation: 105° – 45° = 60°, as it equals the sum of the two non-adjacent angles.
12. Question: In a triangle, angles are 45°, 45°, and 90°. Exterior angle at the 90° vertex:
A. 90°
B. 135°
C. 90° (again)
D. 45°
Answer: A. 90°
Explanation: It is 45° + 45° = 90°.
13. Question: Exterior angle at a vertex is 140°. One non-adjacent interior angle is 60°. The other is:
A. 70°
B. 80°
C. 90°
D. 100°
Answer: B. 80°
Explanation: 140° – 60° = 80°.
14. Question: For angles 35°, 75°, and 70°, exterior angle at 75° vertex:
A. 105°
B. 110°
C. 115°
D. 120°
Answer: A. 105°
Explanation: 35° + 70° = 105°.
15. Question: An exterior angle of 125° has non-adjacent angles of 55° and:
A. 60°
B. 70°
C. 80°
D. 90°
Answer: B. 70°
Explanation: 125° – 55° = 70°.
16. Question: In a triangle with angles 10°, 20°, and 150°, exterior at 150°:
A. 30°
B. 40°
C. 50°
D. 60°
Answer: A. 30°
Explanation: 10° + 20° = 30°.
17. Question: Exterior angle is 115°. One non-adjacent is 50°. Other is:
A. 55°
B. 65°
C. 75°
D. 85°
Answer: B. 65°
Explanation: 115° – 50° = 65°.
18. Question: Angles 60°, 60°, and 60°. Exterior at one vertex:
A. 120°
B. 60°
C. 180°
D. 90°
Answer: A. 120°
Explanation: 60° + 60° = 120°.
19. Question: Exterior angle 145°. Non-adjacent angles sum to:
A. 145°
B. 35°
C. 180°
D. 90°
Answer: A. 145°
Explanation: It equals the sum directly.
20. Question: For angles 25°, 125°, and 30°, exterior at 125°:
A. 55°
B. 65°
C. 75°
D. 85°
Answer: A. 55°
Explanation: 25° + 30° = 55°.
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Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
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