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

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

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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