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 3x, 4x and 5x.

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

According to the question,

5x – 3x = 45

⇒ 2x = 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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