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Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?
- a)44 degrees.
- b)45 degrees.
- c)89 degrees.
- d)90 degrees.
- e)There isn’t enough data to determine
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + ...
If Beta is 90 degrees than Alfa is bigger than 90 and the sum of the angles in the triangle will be bigger than 180 degrees.
Most Upvoted Answer
Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + ...
Understanding the Triangle Angle Sum Property
In any triangle, the sum of the interior angles always equals 180 degrees. Thus, if we denote the angles as Alfa (A), Beta (B), and Gamma (C), the equation can be stated as:
- A + B + C = 180 degrees
Given the condition that Alfa = Beta + Gamma, we can rewrite this as:
- A = B + C
Substituting this into the angle sum property gives us:
- (B + C) + B + C = 180 degrees
This simplifies to:
- 2B + 2C = 180 degrees
Now, dividing by 2:
- B + C = 90 degrees
This implies that the sum of angles Beta and Gamma must always equal 90 degrees.
Analyzing the Options for Beta
Since B + C = 90 degrees, we need to evaluate the options for Beta:
- If Beta = 90 degrees, then C must be 0 degrees (which is not possible in a triangle).
- If Beta is any angle greater than 90 degrees, C would become negative (also impossible).
Thus, Beta can only be less than 90 degrees.
Key Conclusions
- Beta must be less than 90 degrees.
- Therefore, we can eliminate any option that equals or exceeds 90 degrees.
Final Review of Options
- a) 44 degrees: Possible
- b) 45 degrees: Possible
- c) 89 degrees: Possible
- d) 90 degrees: Not Possible
- e) There isn’t enough data to determine: Incorrect
Correct Answer
The answer is option D: 90 degrees cannot be the size of Beta in this triangle.
In any triangle, the sum of the interior angles always equals 180 degrees. Thus, if we denote the angles as Alfa (A), Beta (B), and Gamma (C), the equation can be stated as:
- A + B + C = 180 degrees
Given the condition that Alfa = Beta + Gamma, we can rewrite this as:
- A = B + C
Substituting this into the angle sum property gives us:
- (B + C) + B + C = 180 degrees
This simplifies to:
- 2B + 2C = 180 degrees
Now, dividing by 2:
- B + C = 90 degrees
This implies that the sum of angles Beta and Gamma must always equal 90 degrees.
Analyzing the Options for Beta
Since B + C = 90 degrees, we need to evaluate the options for Beta:
- If Beta = 90 degrees, then C must be 0 degrees (which is not possible in a triangle).
- If Beta is any angle greater than 90 degrees, C would become negative (also impossible).
Thus, Beta can only be less than 90 degrees.
Key Conclusions
- Beta must be less than 90 degrees.
- Therefore, we can eliminate any option that equals or exceeds 90 degrees.
Final Review of Options
- a) 44 degrees: Possible
- b) 45 degrees: Possible
- c) 89 degrees: Possible
- d) 90 degrees: Not Possible
- e) There isn’t enough data to determine: Incorrect
Correct Answer
The answer is option D: 90 degrees cannot be the size of Beta in this triangle.
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Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer?.
Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer?.
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Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + Gamma, what can’t be the size of Beta?a)44 degrees.b)45 degrees.c)89 degrees.d)90 degrees.e)There isn’t enough data to determineCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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