Question

the three angles of a quadrilateral are in the ratio 2:3:5 if the measure of fourth angle is same as the measure of smallest angle among the three then find the all the angles of a quadrilateral

Answer 1

∵ Ratio of three angles is given 2 : 3 : 5

Let the angles be 2x, 3x, 5x

Here smallest angle = 2x

Hence fourth angle of the quadrilateral is also 2x

Now

Sum of all angles of a quadrilateral = 360°

∴ 2x + 2x + 3x + 5x = 360°

12x = 360°

x = 30°

∴ 2x = 60°, 3x = 90°, 5x = 150°

Hence four angles of given quadrilateral are 60°, 60°, 90° and 150°