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An exterior angle of a triangle is 80° and two interior opposite angles are equal. Measure of each of these angles is :
- a)120°
- b)60°
- c)40°
- d)100°
Correct answer is option 'C'. Can you explain this answer?
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An exterior angle of a triangle is 80°and two interior opposite an...
In a triangle, the sum of the measures of the exterior angles is always 360 degrees. Since one of the exterior angles is given as 80 degrees, the sum of the other two exterior angles must be 360 - 80 = 280 degrees.
However, the exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, if one exterior angle is 80 degrees, the sum of the two opposite interior angles must also be 80 degrees.
Let's represent the three interior angles of the triangle as A, B, and C. Since the sum of all interior angles of a triangle is always 180 degrees, we can write the equation:
A + B + C = 180
We know that A + B = 80, so we can substitute this into the equation:
80 + C = 180
Subtracting 80 from both sides, we get:
C = 180 - 80 = 100
So, the two opposite interior angles are 80 and 100 degrees, and the third interior angle can be found using the equation:
A + B + C = 180
A + 80 + 100 = 180
A + 180 = 180
A = 0
Therefore, the three interior angles of the triangle are 0, 80, and 100 degrees.
However, the exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, if one exterior angle is 80 degrees, the sum of the two opposite interior angles must also be 80 degrees.
Let's represent the three interior angles of the triangle as A, B, and C. Since the sum of all interior angles of a triangle is always 180 degrees, we can write the equation:
A + B + C = 180
We know that A + B = 80, so we can substitute this into the equation:
80 + C = 180
Subtracting 80 from both sides, we get:
C = 180 - 80 = 100
So, the two opposite interior angles are 80 and 100 degrees, and the third interior angle can be found using the equation:
A + B + C = 180
A + 80 + 100 = 180
A + 180 = 180
A = 0
Therefore, the three interior angles of the triangle are 0, 80, and 100 degrees.
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An exterior angle of a triangle is 80°and two interior opposite angles are equal. Measure of each of these angles is :a)120°b)60°c)40°d)100°Correct answer is option 'C'. Can you explain this answer?
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An exterior angle of a triangle is 80°and two interior opposite angles are equal. Measure of each of these angles is :a)120°b)60°c)40°d)100°Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about An exterior angle of a triangle is 80°and two interior opposite angles are equal. Measure of each of these angles is :a)120°b)60°c)40°d)100°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An exterior angle of a triangle is 80°and two interior opposite angles are equal. Measure of each of these angles is :a)120°b)60°c)40°d)100°Correct answer is option 'C'. Can you explain this answer?.
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