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In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal to
- a)100°
- b)125°
- c)80°
- d)45°
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a triangle, two angles measure 45° and 55°. The exterior angle at t...
Third interior angle = 180 − (45 + 55) = 80°
Exterior angle = 180 − 80 = 100°
Exterior angle = 180 − 80 = 100°
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In a triangle, two angles measure 45° and 55°. The exterior angle at t...
Understanding Triangle Angles
In any triangle, the sum of the interior angles is always 180 degrees. Given two angles in the triangle, we can find the third angle easily.
Step 1: Calculate the Third Angle
- The two given angles are 45° and 55°.
- To find the third angle (let's call it C), we use the formula:
C = 180° - (45° + 55°)
- Simplifying the equation:
C = 180° - 100° = 80°
Thus, the angles of the triangle are 45°, 55°, and 80°.
Step 2: Finding the Exterior Angle
The exterior angle at any vertex of a triangle is equal to the sum of the two opposite interior angles.
Step 3: Calculate the Exterior Angle at the Third Vertex
- For the third vertex (where the angle is 80°), the exterior angle can be calculated as:
Exterior Angle = 45° + 55°
- Simplifying gives us:
Exterior Angle = 100°
Conclusion
Therefore, the exterior angle at the third vertex is 100°. This means the correct answer is option 'A'.
Understanding these relationships between interior and exterior angles is crucial for solving problems related to triangles in geometry.
In any triangle, the sum of the interior angles is always 180 degrees. Given two angles in the triangle, we can find the third angle easily.
Step 1: Calculate the Third Angle
- The two given angles are 45° and 55°.
- To find the third angle (let's call it C), we use the formula:
C = 180° - (45° + 55°)
- Simplifying the equation:
C = 180° - 100° = 80°
Thus, the angles of the triangle are 45°, 55°, and 80°.
Step 2: Finding the Exterior Angle
The exterior angle at any vertex of a triangle is equal to the sum of the two opposite interior angles.
Step 3: Calculate the Exterior Angle at the Third Vertex
- For the third vertex (where the angle is 80°), the exterior angle can be calculated as:
Exterior Angle = 45° + 55°
- Simplifying gives us:
Exterior Angle = 100°
Conclusion
Therefore, the exterior angle at the third vertex is 100°. This means the correct answer is option 'A'.
Understanding these relationships between interior and exterior angles is crucial for solving problems related to triangles in geometry.
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In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer? for Class 7 2026 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 7 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer?.
In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer? for Class 7 2026 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 7 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle, two angles measure 45° and 55°. The exterior angle at the third vertex is equal toa)100°b)125°c)80°d)45°Correct answer is option 'A'. Can you explain this answer?.
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