Question

Q. The measures of the angles of a quadrilateral are in the ratio 2:4:5: 7. Find the measure of each of its angles.
step by step explanation​

Answer 1

Answer:

Let the common ratio be x

Since, sum of angles of a Quadrilateral is 360°

we have,

2x + 4x + 5x + 7x = 360°

18x = 360°

x = 360/18

x = 20

Therefore, required angles are

2(20) = 40°

4(20) = 80°

5(20) = 100°

7(20) = 140°

Step-by-step explanation:

Answer 2

Given:

A quadrilateral in

• Ratio = 2 : 4 : 5 : 7

What To Find:

We have to find the measure of the quadrilateral.

Property Used:

Sum of the interior angle = 360°

Solution:

Using the property,

⇒ Sum of the interior angle = 360°

Take x as the common multiple and substitute,

⇒ 2x + 4x + 5x + 7x = 360°

Add the terms,

⇒ 18x = 360°

Take 18 to 360,

⇒ x = 360/18

Divide 360 by 18,

⇒ x = 20°

Now, subtitute the values,

• 2x = 2 × 20 = 40°
• 4x = 4 × 20 = 80°
• 5x = 5 × 20 = 100°
• 7x = 7 × 20 = 140°

∴ Thus, the angles are 40°, 80°, 100° and 140°.