Question

PQRS is a parallelogram. The adjacent angles are in the ratio 2 : 1.State all the angles

Answer 1

adjacent angles of a parallelogram are supplementary. let the common multiple be x
2x+x= 180
3x=180
x=180/3
so x=60
therefore the angles are :
2x= 2*60 =120
&x=60.
the required angle are 120°,120°,60,°60°

Answer 2

The angles of parallelogram are 60°, 60°, 120° and 120°

Given:

PQRS is a parallelogram

The adjacent angles are in the ratio 2 : 1

To find:

State all the angles of parallelogram

Solution:

Given that the ratio of adjacent angles in parallelogram = 2 : 1

Let 2x and x be the two adjacent angles

[ Since they are in 2 : 1 ratio ]

As we know that,

Two Adjacent Angles of a Parallelogram are Supplementary  

⇒ 2x + x = 180°

⇒ 3x = 180°

⇒ x = 180°/3 = 60°

⇒ 2x = 2(60°) = 120°

Therefore, two adjacent angles are 60°, 120°

In a parallelogram the opposite angles are equal

The angle which is opposite to 60° is equals to 60°

The angle which is opposite to 120° is equals to 120°  

Therefore,

The angles of parallelogram are 60°, 60°, 120° and 120°

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