Question

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
please help me​

Answer 1

Answer:

The measures of the angles of a quadrilateral are 40°, 80°, 100° and 140° respectively.

Step-by-step explanation:

Given that:

The measures of the angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7.

• Let the first angle of the quadrilateral = 2x
• Second angle = 4x
• Third angle = 5x
• Fourth angle = 7x

We know that:

Sum of all the angles of a quadrilateral = 360°

According to the question:

→ 2x + 4x + 5x + 7x = 360°

→ 18x = 360°

→ x = 360°/18

→ x = 20°

∴ Angles of quadrilateral are:

First angle = 2x = 2 × 20° = 40°

Second angle = 4x = 4 × 20° = 80°

Third angle = 5x = 5 × 20° = 100°

Fourth angle = 7x = 7 × 20° = 140°

Answer 2

Answer:

Given :-

• The angles of Quardilateral in ratio 2:4:5:7

To Find :-

All angles

Solution :-

Let the angles be 2x,4x,5x and 7x

As we know that

Sum of angles in Quadrilateral is 360⁰

$\sf \: 360 = 2x + 4x + 5x + 7x$

$\sf \: 360 = 18x$

$\sf \: x \: = \dfrac{360}{18}$

$\frak \pink{x = 20}$

Angles are :-

2x = 2(20) = 40⁰

4x = 4(20) = 80⁰

5x = 5(20) = 100⁰

7x = 7(20) = 140⁰