Here, we have to find whether the consecutive angles of a parallelogram are equal, complementary or supplementary. We will first draw the parallelogram and define the terms in the option. Then we will list out the properties and find which option is correct. A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. Complete Complete Step by Step Solution:
Let ABCD be the parallelogram.
Now we will define the terms given in the option.
If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
We will now list down all the properties of a parallelogram.
We know that the six properties of a parallelogram are as follows:
1. Opposite sides are congruent.
2. Opposite angles are congruent.
3. Consecutive angles are supplementary.
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent.
When two lines are crossed by another line the pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles. Therefore, the consecutive angles of a parallelogram are supplementary.Note:
Complementary angles are not defined for linear pairs of angles whereas supplementary angles are defined for linear pairs of angles. A square and a rectangle are two shapes which have similar properties of a parallelogram. Both have their opposite sides equal and parallel to each other. Diagonals of both the shapes bisect each other. If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus. A special case of a parallelogram that has its opposite sides parallel to each other but adjacent sides are of unequal lengths. Also, the angles are equal to 90 degrees. If there is one parallel side and the other two sides are non-parallel, then it is a trapezium.