Question

The angles of a quadrilateral are in the ratio of 2:5:5:6 . Find the greatest angle​

Answer 1

⛦ Given :

• Angles of quadrilateral are in ratio 2 : 5 : 5 : 6.

⛦ To find :

• The greatest angle of the Quadrilateral.

⛦ Solution :

Let's assume the angles of the Quadrilateral be :

• 2x
• 5x
• 5x
• 6x

We know that,

•Sum of all angles of quadrilateral is 360°

Therefore,

According to Question,

2x + 5x + 5x + 6x = 360°

18x = 360°

x = 360/18

x = 20°

Therefore,

• 1st angle = 2x = 2×20 = 40°
• 2nd angle = 5x = 5×20 = 100°
• 3rd angle = 5x = 5×20 = 100°
• 4th angle = 6x = 6×20 = 120°

Here, the greatest angle of the Quadrilateral is 4th angle that is 120°.

_______________

Let's verify the angles.

Sum of all anglea of quadrilateral = 360°

40° + 100° + 100° + 120° = 360°

360° = 360°

Hence, L.H.S. = R.H.S.

Thus, checked.

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Answer 2

Given:

The angles of a quadrilateral which are in the ratio of 2 : 5 : 5 : 6.

What to find?

The greatest angle of the quadrilateral.

How to find?

To find the angles of the quadrilateral, first take a variable as the common measures of the quadrilateral. Then use the property of the sum of interior angles of a quadrilateral which is equal to 360°.

Solution:

Let x be the common measures.

Sum of interior angles of a quadrilateral = 360°

⇒ 2x + 5x + 5x + 6x = 360°

Add the terms in LHS,

⇒ 18x = 360°

Take 18 to RHS,

⇒ x = $\frac{360}{18}$

Divide 360 by 18,

⇒ x = 20

Now substitute the value,

• 1st angle = 2x = 2(20) = 40°
• 2nd angle = 5x = 5(20) = 100°
• 3rd angle = 5x = 5(20) = 100°
• 4th angle = 6x = 6(20) = 120°

∴ Hence, The fourth angle is the greatest angle i.e 120°.