Three angles of a quadrilateral are in the ratio 3:4:5. The difference of the least and the greatest of these angles is 45. Find all the four angles of the quadrilateral.

The ratio of the three angles of quadrilateral = 3 : 4 : 5

Let the angles be 3*x*, 4*x* and 5*x.*

The greatest angle among these is 5*x* and the least is 3*x.*

According to the question,

5*x* – 3*x* = 45

⇒ 2*x* = 45

⇒ *x* = 45 ÷ 2

⇒ *x* = 22.5

Hence, the three angles of quadrilateral are 3 × 22.5 = **67.5°**, 4 × 22.5° = **90°** and 5 × 22.5° = **112.5°**.

Fourth angle of quadrilateral = 360° – 67.5° + 90° + 112.5° = 360° – 270° = **90°**

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