Class 9 Exam > Class 9 Questions > Which is true?a)A triangle can have two obtus...
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Which is true?
- a)A triangle can have two obtuse angles
- b)A triangle can have two right angles.
- c)An exterior angle of a triangle is less than either of the interior opposite angles.
- d)A triangle can have two acute angles.
Correct answer is option 'D'. Can you explain this answer?
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Which is true?a)A triangle can have two obtuse anglesb)A triangle can ...
True, you may have a triangle with two or more acute angles. If a triangle has three acute angles, the triangle is called an Acute Triangle. If a triangle has two acute angles and a single obtuse angle, the triangle is called an Obtuse Triangle.
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Which is true?a)A triangle can have two obtuse anglesb)A triangle can ...
Explanation:
Triangle:
A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees.
Options:
a) A triangle can have two obtuse angles:
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. If a triangle has two obtuse angles, the sum of those angles would be more than 180 degrees, which violates the property of a triangle. Therefore, option 'a' is not true.
b) A triangle can have two right angles:
A right angle is an angle that measures exactly 90 degrees. If a triangle has two right angles, the sum of those angles would be 180 degrees, which satisfies the property of a triangle. Therefore, option 'b' is true.
c) An exterior angle of a triangle is less than either of the interior opposite angles:
An exterior angle of a triangle is formed by extending one side of the triangle. It is always greater than either of the interior opposite angles. Therefore, option 'c' is not true.
d) A triangle can have two acute angles:
An acute angle is an angle that measures less than 90 degrees. If a triangle has two acute angles, the sum of those angles would be less than 180 degrees, which satisfies the property of a triangle. Therefore, option 'd' is true.
Conclusion:
Among the given options, option 'D' is the only true statement. A triangle can have two acute angles.
Triangle:
A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees.
Options:
a) A triangle can have two obtuse angles:
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. If a triangle has two obtuse angles, the sum of those angles would be more than 180 degrees, which violates the property of a triangle. Therefore, option 'a' is not true.
b) A triangle can have two right angles:
A right angle is an angle that measures exactly 90 degrees. If a triangle has two right angles, the sum of those angles would be 180 degrees, which satisfies the property of a triangle. Therefore, option 'b' is true.
c) An exterior angle of a triangle is less than either of the interior opposite angles:
An exterior angle of a triangle is formed by extending one side of the triangle. It is always greater than either of the interior opposite angles. Therefore, option 'c' is not true.
d) A triangle can have two acute angles:
An acute angle is an angle that measures less than 90 degrees. If a triangle has two acute angles, the sum of those angles would be less than 180 degrees, which satisfies the property of a triangle. Therefore, option 'd' is true.
Conclusion:
Among the given options, option 'D' is the only true statement. A triangle can have two acute angles.
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Which is true?a)A triangle can have two obtuse anglesb)A triangle can have two right angles.c)An exterior angle of a triangle is less than either of the interior opposite angles.d)A triangle can have two acute angles.Correct answer is option 'D'. Can you explain this answer?
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