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Which of the following is true for the adjacent angles of a parallelogram?
- a)they are equal to each other
- b)they are complementary angles
- c)they are supplementary angles
- d)none of these.
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is true for the adjacent angles of a parallelog...
The solution explains why the adjacent angles of a parallelogram are supplementary:
- In a parallelogram, adjacent angles are on the same side of a transversal line.
- Such angles are known as co-interior angles, and they add up to 180 degrees.
- In this question: One angle is 50 degrees, the adjacent angle will be 130 degrees because 180 - 50 = 130.
Therefore, the adjacent angles are supplementary.
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Which of the following is true for the adjacent angles of a parallelog...
Understanding Adjacent Angles in a Parallelogram
Adjacent angles in a parallelogram have specific properties that stem from its geometric characteristics. A parallelogram is defined as a quadrilateral with opposite sides that are parallel and equal in length.
Key Properties of Parallelograms:
- Opposite Angles Are Equal: In a parallelogram, the angles opposite to each other are equal. For example, if one angle is 60 degrees, the opposite angle is also 60 degrees.
- Sum of Interior Angles: The sum of all interior angles in any quadrilateral, including parallelograms, is 360 degrees.
Adjacent Angles Are Supplementary:
- Definition of Supplementary Angles: Two angles are said to be supplementary if their sum equals 180 degrees.
- Adjacent Angles in Parallelograms: In a parallelogram, each pair of adjacent angles adds up to 180 degrees. For instance, if one angle measures 70 degrees, the adjacent angle will measure 110 degrees (70 + 110 = 180).
Conclusion:
Thus, the correct answer to the question about the nature of adjacent angles in a parallelogram is option 'C': they are supplementary angles. This property is essential for understanding the relationships between angles in various geometric shapes, especially in parallelograms.
Adjacent angles in a parallelogram have specific properties that stem from its geometric characteristics. A parallelogram is defined as a quadrilateral with opposite sides that are parallel and equal in length.
Key Properties of Parallelograms:
- Opposite Angles Are Equal: In a parallelogram, the angles opposite to each other are equal. For example, if one angle is 60 degrees, the opposite angle is also 60 degrees.
- Sum of Interior Angles: The sum of all interior angles in any quadrilateral, including parallelograms, is 360 degrees.
Adjacent Angles Are Supplementary:
- Definition of Supplementary Angles: Two angles are said to be supplementary if their sum equals 180 degrees.
- Adjacent Angles in Parallelograms: In a parallelogram, each pair of adjacent angles adds up to 180 degrees. For instance, if one angle measures 70 degrees, the adjacent angle will measure 110 degrees (70 + 110 = 180).
Conclusion:
Thus, the correct answer to the question about the nature of adjacent angles in a parallelogram is option 'C': they are supplementary angles. This property is essential for understanding the relationships between angles in various geometric shapes, especially in parallelograms.
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