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

**Given:** Three angles of a quadrilateral are in ratio 3 : 4 : 5

Let the mentioned angles be 3*x*, 4*x*, 5*x*

also

5*x* – 3*x* = 45°

⇒Three angles are 3 × 22.5, 4 × 22.5, 5 × 22.5

= 67.5, 90, 112.5

Now we know that sum of all the angles of quadrilateral is 360°

⇒ fourth angle = 360° – sum of other three angles

= 360° – (67.5° + 90° + 112.5°)

= 360° – 270° = 90°

Hence the four angles of the given quadrilateral are 67.5°, 90°, 112.5° and 90°

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