Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram

Solution:

Let ABCD be a parallelogram as shown below.

In parallelogram ABCD,

• ∠A and ∠D are supplementary since DC is parallel to AB and with transversal DA. (Adjacent angles of a parallelogram are supplementary)
• ∠A and ∠B are supplementary since AD is parallel to BC and with transversal BA. (Adjacent angles of a parallelogram are supplementary)

Sum of adjacent angles = 180°

Let each adjacent angle be x

Since the adjacent angles in a parallelogram are supplementary,

x + x = 180°

2x = 180°

x = 180°/ 2 = 90°

Hence, each adjacent angle is 90 degrees

∠A = ∠B = 90°

∠C = ∠A = 90°

∠D = ∠B = 90°

Thus, each angle of the parallelogram measures 90°

☛ Check: Class 8 Maths NCERT Solutions Chapter 3

Video Solution:

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 6

Summary:

Two adjacent angles of a parallelogram have equal measure. The measure of each of the angles of the parallelogram is 90°

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