Let x be the common multiple.
As per question,
\(\angle\)A = 3x
\(\angle\)B = 5x
\(\angle\)C = 7x
\(\angle\)D = 9x
As we know that, Sum of all four angles of quadrilateral is 360o .
\(\angle\)A + \(\angle\)B + \(\angle\)C + \(\angle\)D = 360°
3x + 5x + 7x + 9x = 360°
24x = 360° X = 360/24
= 15°
\(\angle\)A = 3 × 15° = 45°
\(\angle\)B = 5 × 15° = 75°
\(\angle\)C = 7 × 15° = 105°
\(\angle\)D = 9 × 15° = 135°
So, Angles of quadrilateral are 45°, 75°, 105° and 135°.
