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Can you explain the answer of this question below:
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Practical Geometry, Class 7, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.
Q.
The ____________ of a triangle is equal in measure to the sum of interior opposite angles.
- A:interior angle
- B:exterior angle
- C:angle
- D:None of these
The answer is B.
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Can you explain the answer of this question below:Practice Quiz or MCQ...
Option b because two interior opposite anglers is equal to 1 exterior angle
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Can you explain the answer of this question below:Practice Quiz or MCQ...
Explanation:
To understand why the correct answer is option 'B', let's first define the terms involved in the question.
- Interior Angle: An interior angle of a triangle is an angle formed inside the triangle by any two sides.
- Exterior Angle: An exterior angle of a triangle is an angle formed outside the triangle by extending one of the sides.
Now, let's consider a triangle ABC with interior angles A, B, and C, and exterior angles X, Y, and Z.
Sum of Interior Angles:
According to the triangle angle sum property, the sum of the interior angles of any triangle is always 180 degrees. In other words, A + B + C = 180 degrees.
Opposite Interior Angles:
Opposite interior angles are the pairs of angles that are formed by two intersecting lines. In a triangle, the opposite interior angles are the angles that are on the opposite sides of the third side.
Sum of Interior Opposite Angles:
The sum of the interior opposite angles of a triangle is equal to 180 degrees. This can be proved using the property that the sum of angles on a straight line is 180 degrees.
Exterior Angle:
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In other words, X = B + C, Y = A + C, and Z = A + B.
Relation between Exterior Angle and Sum of Interior Opposite Angles:
Now, if we add up the three exterior angles of a triangle (X + Y + Z), we get:
X + Y + Z = (B + C) + (A + C) + (A + B)
= 2A + 2B + 2C
= 2(A + B + C)
Since A + B + C is equal to 180 degrees (sum of interior angles of a triangle), we can substitute this value into the equation:
X + Y + Z = 2(180 degrees)
= 360 degrees
Therefore, the sum of the three exterior angles of a triangle is always 360 degrees.
Conclusion:
From the above explanation, it is clear that the sum of the interior opposite angles of a triangle is equal to the sum of the exterior angles of a triangle. Hence, the correct answer is option 'B' - Exterior Angle.
To understand why the correct answer is option 'B', let's first define the terms involved in the question.
- Interior Angle: An interior angle of a triangle is an angle formed inside the triangle by any two sides.
- Exterior Angle: An exterior angle of a triangle is an angle formed outside the triangle by extending one of the sides.
Now, let's consider a triangle ABC with interior angles A, B, and C, and exterior angles X, Y, and Z.
Sum of Interior Angles:
According to the triangle angle sum property, the sum of the interior angles of any triangle is always 180 degrees. In other words, A + B + C = 180 degrees.
Opposite Interior Angles:
Opposite interior angles are the pairs of angles that are formed by two intersecting lines. In a triangle, the opposite interior angles are the angles that are on the opposite sides of the third side.
Sum of Interior Opposite Angles:
The sum of the interior opposite angles of a triangle is equal to 180 degrees. This can be proved using the property that the sum of angles on a straight line is 180 degrees.
Exterior Angle:
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In other words, X = B + C, Y = A + C, and Z = A + B.
Relation between Exterior Angle and Sum of Interior Opposite Angles:
Now, if we add up the three exterior angles of a triangle (X + Y + Z), we get:
X + Y + Z = (B + C) + (A + C) + (A + B)
= 2A + 2B + 2C
= 2(A + B + C)
Since A + B + C is equal to 180 degrees (sum of interior angles of a triangle), we can substitute this value into the equation:
X + Y + Z = 2(180 degrees)
= 360 degrees
Therefore, the sum of the three exterior angles of a triangle is always 360 degrees.
Conclusion:
From the above explanation, it is clear that the sum of the interior opposite angles of a triangle is equal to the sum of the exterior angles of a triangle. Hence, the correct answer is option 'B' - Exterior Angle.
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Can you explain the answer of this question below:Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Practical Geometry, Class 7, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.Q.The ____________ of a triangle is equal in measure to the sum of interior opposite angles.A:interior angleB:exterior angleC:angleD:None of theseThe answer is B.
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