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

In front of you the next quadrilateral:

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

AAABBBCCCDDD12060120x

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1

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?

AAABBBCCCDDD12060120x

2

Step-by-step solution

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

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

Solving for x x :

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

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

3

Final Answer

60

Practice Quiz

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It is possible to draw a quadrilateral that is not a rectangle, with the sum of its two adjacent angles equaling 180?

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