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

Follow each step carefully to understand the complete solution

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

The parallelogram ABCD is shown below.

What type of angles are indicated in the figure?

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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