Question

In a parallelogram if one angle measure 60° what will be the other 3

Answer 1

Given :-

• One angle of a parallelogram = 60°

To Find :-

• The Other three angles

Solution :-

The Angle angle sum of a Quadrilateral is 360°

Since a Parallelogram is a Quadrilateral it should be 360°[Angle sum ]

Recall The properties of a Parallelogram

• The opposite sides and angles are equal.

This property is used here,

• In the picture Let B be the Angle = 60°

• The angle opposite to B is D so, by the property of parallelogram it = 60°

$\bold{ \red{★Hence \: < D\: = 60}{} }{}$

Now,

Two angles are Needed again,

Since Angles A and C are equal the angles be x

By Angle sum Property of a Quadrilateral.

• 60+60+x+x = 360°

• 120+2x = 360°

• 2x = 360 - 120

• 2 x = 240

• x = 240/2

• x = 120°

Hence < A and < C = 120°

$\boxed{ \bold{ \red{★The \: angles \: are = 60 \: ,120, 60,120}{} }{} }{}$