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

Follow each step carefully to understand the complete solution

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

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 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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