Question

The angles of a quadrilateral are in the ratio of 3: 2 : 4 :1. Find the angles​

Answer 1

Answer:

The angles are -

• 108°
• 72°
• 144°
• 36°

Step-by-step explanation:

Given :

Ratio of the Angles in Quadrilateral = 3 : 2 : 4 : 1

To find :

Their angles

Solution :

Let the angles be -

• 3x
• 2x
• 4x
• 1x

According to the Angle sum property of Quadrilateral, the sum of all angles in Quadrilateral is 360°.

$\sf{\implies} \: 3x + 2x + 4x + 1x = 360 \\ \sf{\implies} \: 5x + 5x = 360 \\ \sf{\implies} \: 10x = 360 \\ \sf{\implies} \: x = \frac{360}{10} \\ \sf{\implies} \: x = 36$

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\implies} \: 3(36) \\ \sf{\implies} \: 108$

$\rule{300}{1.5}$

★ Value of 2x

$\sf{\implies} \: 2(36) \\ \sf{\implies} \: 72$

$\rule{300}{1.5}$

★ Value of 4x

$\sf{\implies} \: 4(36) \\ \sf{\implies} \: 144$

$\therefore$ The angles are -

• 108°
• 72°
• 144°
• 36°

Answer 2

Answer :-

Angles of the quadrilateral are 36°, 108°, 72° and 144

Explanation :-

Ratio of the angles of quadrilateral = 3 : 2 : 4 : 1

Let the angles of the quadrilateral be 3x, 2x, 4x, 1x

We know that

Sum of all angles of the quadrilateral = 360°

⇒ 3x + 2x + 4x + 1x = 360

⇒ 10x = 360

⇒ x = 360/10

⇒ x = 36

One of the angle = x = 36°

Second angle = 3x = 3(36) = 108°

Third angle = 2x = 2(36) = 72°

Fourth angle = 4x = 4(36) = 144°

Therefore the angles of the quadrilateral are 36°, 108°, 72° and 144°