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 3x, 4x, 5x
also
5x – 3x = 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°