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Properties of a Parallelogram - Property: The adjacent angles in a parallelogram are supplementary.

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The adjacent angles in a parallelogram are supplementary.

Given: ABCD is a parallelogram.

To Prove: Any  adjacent angles of a parallelogram are supplementary.

Proof:

ABCD is a parallelogram.

Then AD BC & AB is transversal, making ∠A and ∠ B interior opposite.

Therefore, [since, sum of the interior angles on the same since of the transversal is ].

DC

Similarly,  & 

Thus, The sum of any  adjacent angles of a parallelogram is .

Hence, Any  adjacent angles of a parallelogram are supplementary.

Hence Proved.

Example

In a parallelogram RING, if m∠R = 70°, find all the other angles.
Given: m∠R = 70°
Then, m∠N = 70°
because ∠R and ∠N are opposite angles of a parallelogram.
Since ∠R and ∠I are supplementary,
m∠I = 180° – 70° = 110°
Also, m∠G = 110° since ∠G is opposite to ∠I
Thus, m∠R = m∠N = 70° and m∠I = m∠G = 110°.
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