Question

The ratio of four angles of a quadrilateral is 1:2:3:41:2:3:4 . then the measure of its greater angle is

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Answer 1

Answer:-

Given:

Ratio of four angles of a Quadrilateral are in the ratio 1 : 2 : 3 : 4.

Let the measures of the angles be x , 2x , 3x , 4x.

We know that,

Sum of four angles of a Quadrilateral = 360°

Hence,

⟶ x + 2x + 3x + 4x = 360°

⟶ 10x = 360°

⟶ x = 360/10

⟶ x = 36

Now,

greatest angle = 4x = 4(36) = 144°.

Hence, the measure of the greatest angle is 144°.

Additional Information:-

• A closed figure bounded by four line segments is called a Quadrilateral.

• Sum of four angles of a Quadrilateral = 360°.

• There are different types of quadrilaterals based on sides and angles.

• The line segments joining the opposite vertices of a Quadrilateral are called Diagonals.

Answer 2

Answer:

• Ratio of Four Angles of a Quadrilateral is given as 1 : 2 : 3 : 4
• Then Find Measure of it's Greater Angle.

Let the Angles be x, 2x, 3x & 4x respectively.

• According to the Question :

⇒ Sum of all angles of Quadrilateral = 360°

⇒ x + 2x + 3x + 4x = 360°

⇒ 10x = 360°

• Dividing both term by 10

⇒ x = 36°

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• Measure of Angles of Quadrilateral :

⇢ x = 36°

⇢ 2x = 2(36°) = 72°

⇢ 3x = 3(36°) = 108°

⇢ 4x = 4(36°) = 144°

∴ Measure of Greater Angle is 144°.