Question

The angles of a quadrilateral taken in order are 2x, 3x, 7x, 8x. Find x and prove that two opposite sides are parallel.

Answer 1

this is the correct value of x

Answer 2

Given : The angles of a quadrilateral taken in order are 2x, 3x, 7x, 8x.

To Find:  x and prove that two opposite sides are parallel.

Solution:

Sum of all the angles on a quadrilateral is 360°

Hence 2x + 3x + 7x + 8x  = 20x   = 360°

=>  x= 18°

angles are  36° , 54°  , 126° , 144°

54°  + 126° = 180°

These are adjacent angle

Hence one pair of opposite sides is parallel

as co interior angles are supplementary

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