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

Question

In front of you the next quadrilateral:

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

AAABBBCCCDDD12060120x

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 .

Answer

60

More Questions

Related Subjects

Parallelogram

Question Types

Characteristics and Proofs of a Parallelogram: In order for the quadrilateral to be a parallelogram what should the value of the unknown be ?