To Find Angles Of Quadrilateral When Their Ratio Given

Question 1

The angles of quadrilateral are in the ratio 1 : 2 : 3 : 4 , then find the measures of each angle?

Explanation

The ratio of angle of quadrilateral is = 1 : 2 : 3 : 4

Let, the measures of each angle be 1a, 2a, 3a, 4a
1a + 2a + 3a + 4a = 360 (As we know that, the  sum of the angles of a quadrilateral is 360˚)
10a = 360
a = 360/10

a = 36
So, 1st angle = 1a = 1 x 36 = 36˚
2nd angle = 2a = 2 x 36 = 72˚
3rd angle = 3a = 3 x 36 = 108˚
4th angle = 4a = 4 x 36 = 144˚
Hence, angles of Quadrilateral are 36˚ , 72˚ , 108˚ and 144˚




Question 2

The angles of quadrilateral are in the ratio 12 : 4 : 15 : 5, then find the measures of each angle?

Explanation

The ratio of angle of quadrilateral is = 12 : 4 : 15 : 5
Let, the measures of each angle be 12a , 4a , 15a , 5a
12a + 4a + 15a + 5a = 360 (As we know that, the  sum of the angles of a quadrilateral is 360˚)
36a = 360
a = 360/36

a = 10
So, 1st angle = 12a = 12 x 10 = 120˚
2nd angle = 4a = 4 x 10 = 40˚
3rd angle = 15a = 15 x 10 = 150˚
4th angle = 5a = 5 x 10 = 50˚
Hence, angles of Quadrilateral are 120˚ , 40˚ , 150˚ and 50˚

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