Question

Four angles of a quadrilateral ABCD are in ratio of 3: 5: 7: 9. Find the measure of angles.
I need in step by step solution ​

Answer 1

Answer:

3x + 5x + 7x + 9x = 360°

24x = 360°

x = = 15°

Hence, the angles are 3 x 15° = 45°

5 x 15° = 75°

7 x 15° = 105°

9 x 15° = 135°

Answer 2

Let the angles of quadrilateral be 3x, 5x, 7x, and 9x

We know,

$\sf3x + 5x + 7x + 9x = 360 \\ \sf \to \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 24x = 360 \\ \sf \to \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{24x}{24} = \frac{360}{24} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{30}{2} = 15$

Hence,

• 1st angle of quadrilateral = 45°
• 2nd angle of quadrilateral = 75°
• 3rd angle of quadrilateral = 105°
• 4th angle of quadrilateral = 135°