Given :-

MEASUREMENTS of the adjacent angles of a parallelogram are in the ratio of 3:2

Required to FIND :-

• Measurements of the all four angles ?

Condition used :-

Here condition refer to the properties of the geometrical figures ;

• Sum of 2 adjacent angles in a parallelogram is supplementary .

• Opposite angles are equal .

Solution :-

Since in the question it is not mentioned that the parallelogram has some labelling .

So,

Let's consider the 2 adjacent angles as ;

1st angle & 2nd angle .

Measurements of the adjacent angles of a parallelogram are in the ratio of 3:2

So,

Let the first angle be 3x

second angle be 2x

According to problem ;

3x + 2x = 180°

[ Reason :- Since, sum of two adjacent angles in a parallelogram is supplementary ]

5x = 180°

x = 180°/5

x = 36°

Hence,

Value of x is 36°

This implies ;

• 1st angle = 3x = 3(36°) = 108°

• 2nd angle = 2x = 2( 36° ) = 72°

Similarly,

we also know that ;

In a parallelogram,

• opposite angles are also equal

Which implies ;

1st angle = 3rd angle

=> 3rd angle = 108°

2nd angle = 4TH angle

=> 4th angle = 72°

Therefore,

Measurement of all 4 angles are ;

108° , 72° , 108° & 72°

Know more :-

What is a ratio ?

A ratio is nothing but it is a method of comparison between any two things .

The comparison can be on any aspect whether it can be on weight , age , height ETC .

A parallelogram is a type of quadrilateral .

And , a quadrilateral is a type of polygon .

we have different quadrilaterals DEPENDING upon their properties .

They are ;

• Parallelogram

• Rectangle

• Square

• Trapezium

• Rhombus

• Kite

These all geometrical figures are made up of 4 line segments .

They have some alike properties and different properties .

But,

The sum of all angles in a quadrilateral is 360°