the measure of adjacent angle of a parallelogram are in the ratio 3:2 find all the angles
Answers
adjacent angles of parallelogram = 180
let each angle be 'x'
3x + 2x = 180
5x = 180
x= 180/5
x=36
first angle= 36*3=108
second angle= 36*2= 72
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°