Find the Missing Angle X: Converting a Quadrilateral into a Parallelogram with 60° and 120° Angles

Q: Why aren't all angles in a parallelogram equal?

Only rectangles have all angles equal (90° each). In a general parallelogram, opposite angles are equal, but consecutive angles are supplementary.

Q: How do I remember which angles are supplementary?

Think of consecutive angles as neighbors - they're next to each other and must add up to $ 180° $. Opposite angles are across from each other and are equal.

Q: Can a parallelogram have all acute angles?

No! If consecutive angles are supplementary and one is acute (less than 90°), its neighbor must be obtuse (greater than 90°) to reach $ 180° $.

Q: Is there a quick way to find the missing angle?

Yes! Since consecutive angles add to $ 180° $, just subtract the given angle from 180°: $ x = 180° - 120° = 60° $

Parallelogram Properties with Consecutive Angles

In front of you the next quadrilateral:

What should the value of x be for the quadrilateral ABCD to be 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:

What should the value of x be for the quadrilateral ABCD to be a parallelogram?

Step-by-step solution

In a parallelogram, consecutive angles are supplementary, which means they add up to $180^\circ$ . Given that $\angle C = 120^\circ$ , the angle $\angle D = x$ must fulfill the equation:

180^\circ = \angle C + \angle D = 120^\circ + x

Solving for $x$ :

x = 180^\circ - 120^\circ = 60^\circ

Therefore, the value of $x$ that makes $ABCD$ a parallelogram is $x = 60^\circ$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Consecutive angles in a parallelogram are supplementary
Technique: Set up equation: $120° + x = 180°$
Check: Verify opposite angles equal: both 60° and both 120° ✓

Common Mistakes

Avoid these frequent errors

Assuming all angles in a parallelogram are equal
Don't think all four angles must be the same = wrong 90° assumption! Only opposite angles are equal in parallelograms, not all four. Always remember consecutive angles are supplementary (add to 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

Why aren't all angles in a parallelogram equal?

Only rectangles have all angles equal (90° each). In a general parallelogram, opposite angles are equal, but consecutive angles are supplementary.

How do I remember which angles are supplementary?

Think of consecutive angles as neighbors - they're next to each other and must add up to $180°$ . Opposite angles are across from each other and are equal.

What if I get an angle greater than 180°?

That's impossible for interior angles! Check your work - you might have confused which angles are consecutive. Interior angles in any quadrilateral are always less than $180°$ .

Can a parallelogram have all acute angles?

No! If consecutive angles are supplementary and one is acute (less than 90°), its neighbor must be obtuse (greater than 90°) to reach $180°$ .

Is there a quick way to find the missing angle?

Yes! Since consecutive angles add to $180°$ , just subtract the given angle from 180°: $x = 180° - 120° = 60°$

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