Consecutive angles of a Parallelogram area)Supplementaryb)Acutec)Complementaryd)EqualCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Option A (supplementary)As one of the basic properties of parallelograms is that any pair of consecutive angles are supplementary.

Answer

The sum of two consecutive angles are always supplementary and equal to 180• they are also called allied angle

Answer

No,the correct answer is option (c), because consecutive means one below each other in parellogram ie is complementry angle sum of two angles =90

Answer

Consecutive Angles of a Parallelogram are Supplementary

A parallelogram is a quadrilateral with opposite sides parallel. When considering the angles of a parallelogram, there are several important properties to note. One of these properties is that the consecutive angles of a parallelogram are supplementary, meaning that they add up to 180 degrees.

Definition of a Parallelogram:
A parallelogram is a quadrilateral with opposite sides parallel. This means that the opposite sides of a parallelogram are equal in length and the opposite angles are equal in measure.

Consecutive Angles:
Consecutive angles of a parallelogram are the angles that are next to each other, sharing a side. For example, in the parallelogram ABCD, angle A and angle B are consecutive angles, as are angle B and angle C, angle C and angle D, and angle D and angle A.

Supplementary Angles:
Supplementary angles are a pair of angles whose measures add up to 180 degrees. In other words, if the measure of one angle is x degrees, then the measure of its supplementary angle is 180 - x degrees.

Explanation of the Property:
In a parallelogram, the opposite angles are equal in measure. Let's consider the consecutive angles of a parallelogram:

1. Angle A and Angle B: Since angle A and angle B are consecutive angles, they share the side AB. By the definition of a parallelogram, opposite sides are parallel, so we can conclude that angle A and angle B are also opposite angles. Therefore, angle A and angle B are equal in measure.

2. Angle B and Angle C: Similarly, angle B and angle C are consecutive angles. They share the side BC, which is also a side of the parallelogram. Since opposite sides of a parallelogram are parallel, we can conclude that angle B and angle C are opposite angles and therefore equal in measure.

By applying the same reasoning to the remaining consecutive angles (angle C and angle D, and angle D and angle A), we can see that all consecutive angles of a parallelogram are equal in measure.

Conclusion:
In a parallelogram, the consecutive angles are equal in measure. Since the sum of the measures of any pair of consecutive angles is equal to 180 degrees, we can conclude that the consecutive angles of a parallelogram are supplementary. Therefore, the correct answer is option 'A' - Supplementary.

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