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°