Class 7 Exam > Class 7 Questions > Which of the following statements is incorrec...
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Which of the following statements is incorrect?
- a)The sum of angles in a triangle is 2 right angles.
- b)The exterior angle of a triangle is equal to the interior angle of the triangle.
- c)The hypotenuse is the longest side of a right angled triangle.
- d)All the above.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements is incorrect?a)The sum of angles in ...
The correct answer is option B because in option B it is written that the Exterior angle of a triangle is equal to the interior angle of the triangle. But not fully correct because the sum of any two interior angles of a triangle cannot be equal to Exterior angle of the triangle. Exterior angle of a triangle is equal to the sum of interior opposite angles of the triangle. Hence option B is incorrect
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Which of the following statements is incorrect?a)The sum of angles in ...
Explanation:
Statement a: The sum of angles in a triangle is 2 right angles.
This statement is correct. The sum of angles in any triangle is always equal to 180 degrees, which is equivalent to 2 right angles. This is a fundamental property of triangles.
Statement b: The exterior angle of a triangle is equal to the interior angle of the triangle.
This statement is incorrect. The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is always greater than any of the interior angles of the triangle. The exterior angle is equal to the sum of the two non-adjacent interior angles of the triangle.
Statement c: The hypotenuse is the longest side of a right-angled triangle.
This statement is correct. In a right-angled triangle, the hypotenuse is the side opposite the right angle. It is always the longest side in the triangle. This can be proven using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Conclusion:
Based on the explanation above, the incorrect statement is option 'B': The exterior angle of a triangle is equal to the interior angle of the triangle. This is incorrect because the exterior angle is always greater than any of the interior angles of a triangle.
Statement a: The sum of angles in a triangle is 2 right angles.
This statement is correct. The sum of angles in any triangle is always equal to 180 degrees, which is equivalent to 2 right angles. This is a fundamental property of triangles.
Statement b: The exterior angle of a triangle is equal to the interior angle of the triangle.
This statement is incorrect. The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is always greater than any of the interior angles of the triangle. The exterior angle is equal to the sum of the two non-adjacent interior angles of the triangle.
Statement c: The hypotenuse is the longest side of a right-angled triangle.
This statement is correct. In a right-angled triangle, the hypotenuse is the side opposite the right angle. It is always the longest side in the triangle. This can be proven using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Conclusion:
Based on the explanation above, the incorrect statement is option 'B': The exterior angle of a triangle is equal to the interior angle of the triangle. This is incorrect because the exterior angle is always greater than any of the interior angles of a triangle.
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