The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find all the interior angles of the pentagon
Answers
In the above Question , the following information is given -
The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5.
To find -
Find all the interior angles of the Pentagon.
Solution -
The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5.
Let these angles be x, 2x, 3x, 4x and 5x respectively.
So, the sum of the angles are as follows -
=> x + 2x + 3x + 4x + 5x
=> 15x.
But , we know that for any polygon , the sum of all exterior angles is 360°
=> 15x = 360°
=> x = 24°
The interior angle corresponding to x -
=> ( 180° - x )
=> 156°
The interior angle corresponding to 2x -
=> ( 180° - 2x )
=> 132°
The interior angle corresponding to 3x -
=> ( 180° - 3x )
=> 108°
The interior angle corresponding to 4x -
=> ( 180° - 4x )
=> 84°
The interior angle corresponding to 5x -
=> ( 180° - 5x )
=> 60°
This is the required answer.
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Answer:
GIVEN :-
The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5.
TO FIND :-
Find all the interior angles of the Pentagon.
SOLUTION -
The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5.
Let these angles be x, 2x, 3x, 4x and 5x respectively.
So, the sum of the angles are as follows -
=> x + 2x + 3x + 4x + 5x
=> 15x.
But , we know that for any polygon , the sum of all exterior angles is 360°
=> 15x = 360°
=> x = 24°
The interior angle corresponding to x -
=> ( 180° - x )
=> 156°
The interior angle corresponding to 2x -
=> ( 180° - 2x )
=> 132°
The interior angle corresponding to 3x -
=> ( 180° - 3x )
=> 108°
The interior angle corresponding to 4x -
=> ( 180° - 4x )
=> 84°
The interior angle corresponding to 5x -
=> ( 180° - 5x )
=> 60°
This is the required answer.