Question

Three angles of a quadrilateral are in ratio 3:5:7:9.find the measure of each of these angles​

Answer 1

Angle A = 3x

Angle B = 5x

Angle C = 7x

Angle D = 9x

So,

A + B + C + D = 360

3x + 5x + 7x + 9x = 360

30x = 360

x = 360/30

x = 12

Now,

Angle A = 3 multi 12 = 36°

Angle B = 5 multi 12 = 60°

Angle C = 7 multi 12 = 84°

Angle D = 9 multi 12 = 108°

Answer 2

$\textsf{\underline{\underline{Answer :-}}}$

The angles of the quadliateral are =

One Angle = 45°

Second Angle = 75°

Third Angle = 105°

Forth Angle = 135°

$\textsf{\underline{\underline{Explanation :-}}}$

Given :

The Ratio = 3:5:7:9

To find :

The Measure of each angle

Solution :

Consider,

One Angle as 3x

Second angle as 5x

Third angle as 7x

Forth Angle as 9x

$\star$ As we know, all angles of a quadliateral sum up and make 360°.

So,

$\tt{\implies}3x + 5x + 7x + 9x = 360$

$\tt{\implies}24x = 360$

$\tt{\implies}x = \dfrac{360}{24}$

$\tt{\implies}x = 15$

Value of 3x

$\tt{\implies}$ 3 × x

$\tt{\implies}$ 3 × 15

$\tt{\implies}$ 45

Value of 5x

$\tt{\implies}$ 5 × x

$\tt{\implies}$ 5 × 15

$\tt{\implies}$ 75

Value of 7x

$\tt{\implies}$ 7 × x

$\tt{\implies}$ 7 × 15

$\tt{\implies}$ 105

Value of 9x

$\tt{\implies}$ 9 × x

$\tt{\implies}$ 9 × 15

$\tt{\implies}$ 135

$\therefore$The angles of the quadliateral are =

One Angle = 45°

Second Angle = 75°

Third Angle = 105°

Forth Angle = 135°

$\textsf{\underline{\underline{Verification :-}}}$

$\tt{\implies}$45° + 75° + 105° + 135° = 360°

$\tt{\implies}$ 360° = 360°

$\therefore$The angles of the quadliateral are =

One Angle = 45°

Second Angle = 75°

Third Angle = 105°

Forth Angle = 135°