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

Question

Philoid · Accepted Answer

Let x be the common multiple.

As per question,

A = 3x

B = 5x

C = 7x

D = 9x

As we know that, Sum of all four angles of quadrilateral is 360^o.

A + B + C + D = 360°

3x + 5x + 7x + 9x = 360°

24x = 360°

X = 360/24

= 15°

A = 3 × 15° = 45°

B = 5 × 15° = 75°

C = 7 × 15° = 105°

D = 9 × 15° = 135°

So, Angles of quadrilateral are 45°, 75°, 105° and 135°.