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If one angle of a triangle is equal to the sum of the other two angles, the triangle must be:
- a)Scalene
- b)Right Angled
- c)Obtuse Angled
- d)Acute Angled
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If one angle of a triangle is equal to the sum of the other two angles...
Explanation:
Right Angled Triangle:
- In a right-angled triangle, one angle is a right angle, which is equal to 90 degrees.
- The other two angles are acute angles, which are less than 90 degrees.
- The sum of the two acute angles in a right-angled triangle is always equal to 90 degrees.
Given condition:
- One angle of the triangle is equal to the sum of the other two angles.
- Let the angles be x, y, and z, where x is the angle that is equal to the sum of y and z.
- Therefore, x = y + z.
- According to the given condition, x = y + z.
Conclusion:
- Since the given condition x = y + z is satisfied in a right-angled triangle, the triangle must be a right-angled triangle.
- Therefore, the correct answer is option 'B' - Right Angled Triangle.
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Community Answer
If one angle of a triangle is equal to the sum of the other two angles...
Let x, y and z is the angles, where x = y + z
x + y + z = 180° (angle sum property)
(y + z) + y + z = 180°
2(y + z)= 180°
x = 90°, hence triangle is right angled.
x + y + z = 180° (angle sum property)
(y + z) + y + z = 180°
2(y + z)= 180°
x = 90°, hence triangle is right angled.
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If one angle of a triangle is equal to the sum of the other two angles, the triangle must be:a)Scalene b)Right Angledc)Obtuse Angled d)Acute AngledCorrect answer is option 'B'. Can you explain this answer?
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