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The exterior angle of a triangle is equal to the sum of two
- a)alternate angles.
- b)interior angles
- c)exterior angles
- d)interior opposite angles
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The exterior angle of a triangle is equal to the sum of twoa)alternate...
∠1 + ∠2 + ∠3 = 180o (Angle sum property)....(a)
∠3 + ∠4 = 180o (Linear Pair)....(b)
On equating equations a and b, we get
∠1 + ∠2 = ∠4
Most Upvoted Answer
The exterior angle of a triangle is equal to the sum of twoa)alternate...
Exterior Angle of a Triangle:
The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is the angle formed between the extended side and the adjacent interior angle.
Explanation:
To understand why the correct answer is option 'D', let's consider the properties of alternate angles, interior angles, exterior angles, and interior opposite angles in a triangle.
1. Alternate Angles:
Alternate angles are formed when a transversal intersects two parallel lines. In a triangle, there are no parallel lines present, so the exterior angle cannot be equal to the sum of alternate angles.
2. Interior Angles:
Interior angles are the angles formed inside the triangle. The sum of the interior angles of a triangle is always 180 degrees. Therefore, the exterior angle cannot be equal to the sum of interior angles.
3. Exterior Angles:
The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is the angle formed between the extended side and the adjacent interior angle. The exterior angle is always equal to the sum of the two opposite interior angles.
4. Interior Opposite Angles:
Interior opposite angles are the angles formed inside the triangle, opposite to the exterior angle. The sum of the interior opposite angles is always equal to the exterior angle.
Therefore, the correct answer is option 'D' - the exterior angle of a triangle is equal to the sum of the two interior opposite angles. This property holds true for all triangles.
The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is the angle formed between the extended side and the adjacent interior angle.
Explanation:
To understand why the correct answer is option 'D', let's consider the properties of alternate angles, interior angles, exterior angles, and interior opposite angles in a triangle.
1. Alternate Angles:
Alternate angles are formed when a transversal intersects two parallel lines. In a triangle, there are no parallel lines present, so the exterior angle cannot be equal to the sum of alternate angles.
2. Interior Angles:
Interior angles are the angles formed inside the triangle. The sum of the interior angles of a triangle is always 180 degrees. Therefore, the exterior angle cannot be equal to the sum of interior angles.
3. Exterior Angles:
The exterior angle of a triangle is formed by extending one of the sides of the triangle. It is the angle formed between the extended side and the adjacent interior angle. The exterior angle is always equal to the sum of the two opposite interior angles.
4. Interior Opposite Angles:
Interior opposite angles are the angles formed inside the triangle, opposite to the exterior angle. The sum of the interior opposite angles is always equal to the exterior angle.
Therefore, the correct answer is option 'D' - the exterior angle of a triangle is equal to the sum of the two interior opposite angles. This property holds true for all triangles.
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The exterior angle of a triangle is equal to the sum of twoa)alternate angles.b)interior anglesc)exterior anglesd)interior opposite anglesCorrect answer is option 'D'. Can you explain this answer?
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