Parallelogram Investigation: Analyzing a Quadrilateral with 70° and 120° Angles

Q: What does 'consecutive angles' mean in a parallelogram?

Consecutive angles are angles that share a common side. In quadrilateral ABCD, angles A and B are consecutive, B and C are consecutive, and so on. They're like neighbors around the shape!

Q: Why must consecutive angles in a parallelogram add to 180°?

This happens because parallel lines create supplementary angles when cut by a transversal. Since opposite sides are parallel in a parallelogram, consecutive angles must be supplementary (sum to 180°).

Q: What if I'm given opposite angles instead of consecutive ones?

Opposite angles in a parallelogram are equal, not supplementary. So if you have angles A = 70° and C = 120°, they should be equal for a parallelogram, but 70° ≠ 120°!

Q: Could this quadrilateral still be some other type of shape?

Yes! It could be a general quadrilateral or even a trapezoid. The question only asks if it can be a parallelogram, which requires very specific angle relationships.

Q: How do I remember all the parallelogram properties?

Think "POSE": Parallel opposite sidesOpposite angles equalSupplementary consecutive anglesEqual opposite sides

Parallelogram Properties with Consecutive Angle Tests

In front of you the next 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

In front of you the next quadrilateral:

Is it possible that it is a parallelogram?

Step-by-step solution

To determine if the quadrilateral is a parallelogram, we need to verify the properties of the angles. A key property of parallelograms is that consecutive angles are supplementary, meaning their sum equals $180^\circ$ .

The problem provides the measures of two consecutive angles: $\angle B = 70^\circ$ and $\angle C = 120^\circ$ .

Next, let's calculate the sum of these angles:
$\angle B + \angle C = 70^\circ + 120^\circ = 190^\circ$

The sum of $\angle B$ and $\angle C$ is $190^\circ$ , which is not equal to $180^\circ$ .

This indicates that the quadrilateral cannot be a parallelogram because two consecutive angles do not add up to $180^\circ$ .

Therefore, the given quadrilateral is not a parallelogram.
Thus, the correct answer is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Consecutive angles in parallelograms must sum to 180°
Technique: Add given angles: 70° + 120° = 190°
Check: Since 190° ≠ 180°, quadrilateral cannot be parallelogram ✓

Common Mistakes

Avoid these frequent errors

Assuming any quadrilateral with given angles is a parallelogram
Don't just look at individual angle measures = missing the key relationship! This ignores the fundamental property that consecutive angles must be supplementary. Always check if consecutive angles sum to exactly 180°.

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 does 'consecutive angles' mean in a parallelogram?

Consecutive angles are angles that share a common side. In quadrilateral ABCD, angles A and B are consecutive, B and C are consecutive, and so on. They're like neighbors around the shape!

Why must consecutive angles in a parallelogram add to 180°?

This happens because parallel lines create supplementary angles when cut by a transversal. Since opposite sides are parallel in a parallelogram, consecutive angles must be supplementary (sum to 180°).

What if I'm given opposite angles instead of consecutive ones?

Opposite angles in a parallelogram are equal, not supplementary. So if you have angles A = 70° and C = 120°, they should be equal for a parallelogram, but 70° ≠ 120°!

Could this quadrilateral still be some other type of shape?

Yes! It could be a general quadrilateral or even a trapezoid. The question only asks if it can be a parallelogram, which requires very specific angle relationships.

How do I remember all the parallelogram properties?

Think "POSE":

Parallel opposite sides
Opposite angles equal
Supplementary consecutive angles
Equal opposite sides

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