Question

Three angles of a quadrilateral are in the ratio 3:2:1. The sum of the smallest and the greatest angle is 180°. Find all the angles of a quadrilateral​

Answer 1

a/c to question,

Three angle of a quadrilateral are in the ratio 3 : 2 : 1.

so, first angle = 3x

2nd angle = 2x

and 3rd angle = x

let another angle is A.

we know, sum of all angle of the quadrilateral = 360°

so, 3x + 2x + x + A = 360°

⇒6x + A = 360° .......(1)

again, smallest angle + largest angle = 180°

or, x + 3x = 180°

or, x = 180°/4 = 45°

so, A = 360° - 6 × 45° = 90°

hence, all angles are ;

3x = 3 × 45° = 135°

2x = 2 × 45° = 90°

x = 1 × 45° = 45°

and A = 90°

Answer 2

Answer:

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