ABCD is a parallelogram in which one angle is 120.find the other three angle.

Question

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Answer 1

adjacent angles of a parallelogram sum to 180º

either adjacent angle to the 120º angle is 60º

opposite angles of a parallelogram are congruent

the other angles are 60º, 120º, and 60º (along with the 120º angle that was given)

Answer 2

You need to know some of the properties of quadrilaterals:

1. The sum of the 4 interior angles is 360^o
2. Adjacent angles are supplementary, meaning that they add to 180^o

 

So if one angle = 120^o, property 2 above tells us that the two angles next to it are 180^o - 120^o = 60^o

So three of the angles are 120^o, 60^o, and 60^o.  Use property 1 above to find the last angle.