Question

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

Answer 1

Step-by-step explanation:

By ASP, sum of all angles is 360°

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

3x+5x+7x+9x=360°

24x=360°

x=15°

So the required angles are:

3x=45°

5x=75°

7x=105°

9x=135°

Answer 2

• The measure of angles of a quadrilateral are 45°, 75°, 105° and 135°.

Given :

• The angles of a quadrilateral are in the ratio = 3 : 5 : 7 : 9.

To Find :

• The measure of each angles of a quadrilateral.

Solution :

Let,

The first angle be 3x.

The second angle be 5x.

The third angle be 7x.

The fourth angle be 9x.

First, we need to find the value of x.

We know that,

Sum of all the angles of a quadrilateral = 360°

I.e.,

$\hookrightarrow \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

Now,

$\hookrightarrow 3x + 5x + 7x + 9x = 360 \degree$

$\hookrightarrow 8x + 16x = 360 \degree$

$\hookrightarrow 24x = 360 \degree$

$\hookrightarrow x = \cancel \dfrac{360 \degree}{24}$

$\hookrightarrow x = \cancel \dfrac{180\degree}{12}$

$\hookrightarrow x = \cancel \dfrac{90 \degree}{6}$

$\hookrightarrow x = \cancel \dfrac{45 \degree}{3}$

$\hookrightarrow x = \dfrac{15\degree}{1}$

$\hookrightarrow x = 15 \degree$

So, the angles of a quadrilateral are :

The first side = 3x = 3 × 15° = 45°.

The second side = 5x = 5 × 15° = 75°.

The third side = 7x = 7 × 15° = 105°.

The fourth side = 9x = 9 × 15° = 135°.

Hence,

The angles of a quadrilateral are 45°, 75°, 105° and 135°.

Verification :

Substitute all the values of angles of a quadrilateral in equation (1),

$\hookrightarrow \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

Now we have,

• $\angle1 = 45 \degree$
• $\angle2 = 75 \degree$
• $\angle3 = 105 \degree$
• $\angle4 = 135 \degree$

$\hookrightarrow 45 \degree + 75 \degree + 105 \degree + 135 \degree = 360 \degree$

$\hookrightarrow 120 \degree + 240 \degree = 360 \degree$

$\hookrightarrow 360 \degree = 360 \degree$

Hence Verified !!