three angles of a quadrilateral are in the ratio 4:5:3.the difference the least and the greatest these angles 45dgree.find all the four angles of the quadrilateral?
Answers
Given :-
Ratio of three angles of the quadrilateral = 4 : 5 : 3
The difference the least and the greatest these angles = 45°
To Find :-
The first angle.
The second angle.
The third angle.
The fourth angle.
Analysis :-
Consider the common ratio as a variable.
Then make an equation according and find the three angles.
To find the fourth angle we've to add the three angles we got and subtract it from the total degree of a quadrilateral.
Solution :-
Consider the common ratio as 'x'. Then the angles would be 4x, 5x and 3x.
We know that,
5x - 3x = 45
2x = 45
x = 45/2
x = 22.5
Substituting the value,
4x = 4 × 22.5 = 90°
5x = 5 × 22.5 = 112.5°
3x = 3 × 22.5 = 65.5°
Finding the third angle,
We know that, sum of a quadrilateral = 360°
Fourth angle = 360 - (Sum of three angles)
= 360 - (90 + 112.5 + 65.5)
= 360 - 270
= 90°
Therefore, the angles are 90°, 112.5°, 65.5° and 90°.
Consider the common ratio as 'x'. Then the angles would be 4x, 5x and 3x.
We know that,
5x - 3x = 45
2x = 45
x = 45/2
x = 22.5
Substituting the value,
4x = 4 × 22.5 = 90°
5x = 5 × 22.5 = 112.5°
3x = 3 × 22.5 = 65.5°
Finding the third angle,
We know that, sum of a quadrilateral = 360°
Fourth angle = 360 - (Sum of three angles)
= 360 - (90 + 112.5 + 65.5)
= 360 - 270
= 90°
Therefore, the angles are 90°, 112.5°, 65.5° and 90°.