Parallelogram Classification: Analyzing a Quadrilateral with 60° and 120° Angles

Q: What if I only know two angles - is that enough?

Yes! If you know two angles are opposite and equal, plus the quadrilateral has other parallelogram properties, that's sufficient. Remember that opposite angles being equal is a key identifying feature.

Q: Do adjacent angles in a parallelogram have any special relationship?

Absolutely! Adjacent angles (like A and B) are supplementary, meaning they add up to $ 180° $. So if angle A = 120°, then angle B must equal 60°.

Q: How do I remember which angles are opposite?

Think of opposite angles as being diagonal from each other. In quadrilateral ABCD, angle A is opposite to angle C, and angle B is opposite to angle D.

Q: What other properties make a quadrilateral a parallelogram?

Opposite sides are parallel and equalDiagonals bisect each otherOne pair of opposite sides is both parallel and equal

Parallelogram Properties with Opposite Angle Pairs

Below is a quadrilateral:

Is it possible that it is a parallelogram?

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Step-by-step written solution

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Understand the problem

Below is a quadrilateral:

Is it possible that it is a parallelogram?

Step-by-step solution

Let's review the property: a quadrilateral in which two pairs of opposite angles are equal is a parallelogram.

From the data in the drawing, it follows that:

$D=B=60$

$A=C=120$

Therefore, the quadrilateral is actually a parallelogram.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Opposite angles in parallelograms are always equal
Technique: Check if angle A = angle C and angle B = angle D
Check: Sum all angles: 120° + 60° + 120° + 60° = 360° ✓

Common Mistakes

Avoid these frequent errors

Only checking adjacent angles instead of opposite angles
Don't compare angles A and B (which are adjacent) = wrong property! Adjacent angles in parallelograms are supplementary (add to 180°), not equal. Always compare opposite angles: A with C, and B with D.

Practice Quiz

Test your knowledge with interactive questions

It is possible to draw a quadrilateral that is not a rectangle, with the sum of its two adjacent angles equaling 180?

FAQ

Everything you need to know about this question

What if I only know two angles - is that enough?

Yes! If you know two angles are opposite and equal, plus the quadrilateral has other parallelogram properties, that's sufficient. Remember that opposite angles being equal is a key identifying feature.

Do adjacent angles in a parallelogram have any special relationship?

Absolutely! Adjacent angles (like A and B) are supplementary, meaning they add up to $180°$ . So if angle A = 120°, then angle B must equal 60°.

How do I remember which angles are opposite?

Think of opposite angles as being diagonal from each other. In quadrilateral ABCD, angle A is opposite to angle C, and angle B is opposite to angle D.

What other properties make a quadrilateral a parallelogram?

Opposite sides are parallel and equal
Diagonals bisect each other
One pair of opposite sides is both parallel and equal

Can a quadrilateral be a parallelogram with different angle measures?

Yes! Parallelograms don't need to have all angles equal (that would be a rectangle). They just need opposite angles equal and adjacent angles supplementary.

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