1.

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

Answer»

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°.



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