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Home >> Parallelogram >> Adjacent Angles of Parallelogram >>

 Area of Parallelogram Opposite Angles of Parallelogram Adjacent Angles of Parallelogram Diagonal Of Parallelogram Difference & Similarity between Rectangle & Parallelogram Difference & Similarity between Square & Parallelogram Difference & Similarity between Square, Rectangle & Parallelogram Properties of Parallelogram

Adjacent Angles in a parallelogram are always supplementary
In other words, we can say:
Sum of Adjacent Angles in a parallelogram is always equal to 180 degree.

Example 1: Observe the parallelogram PQRS

Since we know that sum of adjacent angles in a parallelogram is always equal to 180 degree, so we get:

Angle P + Angle Q = 180 degree
Angle Q + Angle R = 180 degree
Angle R + Angle S = 180 degree
Angle S + Angle P = 180 degree

Example 2: In the given parallelogram ABCD, angle D = 70 degree. Find measure of the remaining angles.

Solution: In the given parallelogram,
Angle D = 70 degree

Since, Adjacent Angles in a parallelogram are always supplementary, so we get:
Angle D + Angle C = 180 degree

Put the values of angle D from above and we get:
70 + Angle C = 180

Subtract 70 from both sides and we get:
Angle C = 110 degree(Statement 1)

Now again from adjacent angle property of parallelogram we get:
Angle C + Angle B = 180 degree

Put the values of angle C from above statement 1 and we get:
110 + Angle B = 180

Subtract 110 from both sides and we get:
Angle B = 70 degree(Statement 2)

Lastly, again apply adjacent angle property of parallelogram and we get:
Angle B + Angle A = 180 degree

Put the values of angle B from above statement 2 and we get:
70 + Angle A = 180

Subtract 70 from both sides and we get:
Angle A = 110 degree