Three angles of the quadrilateral are in the ratio 1:2:3 and the sum of the smallest and the greatest
angle is 180°. Find all the angles of the quadrilateral.
Answers
Given :-
Ratio of the three angles of the quadrilateral = 1 : 2 : 3
The sum of the smallest and the greatest angle = 180°
To Find :-
All the angles of the quadrilateral.
Analysis :-
Consider the common ratio as a variable.
Make an equation accordingly and find the value of the variable.
Substitute the value of the variable in the 3 angles.
Since a quadrilateral has 4 angles consider the 4th angle as a variable.
Make an equation accordingly and find the value of the 4th one.
Solution :-
Consider the common ratio as 'x'. Then the three angles would be x, 2x and 3x.
Given that,
Sum of smallest angle and greatest angle is 180 degree.
Making an equation,
x + 3x = 180°
4x = 180°
x = 180/4
x = 45°
Therefore,
x = 45°
2x = 2 × 45 = 90°
3x = 3 × 45 = 135°
We know that,
Sum of all angles of quadrilateral = 360°
Let the fourth angle be 'y'.
Making an equation,
45 + 90 + 135 + y = 360°
270 + y = 360°
By transposing,
y = 360 - 270
y = 90°
Therefore, the four angles are 45°, 90°, 90° and 135°.