Question

the ratio of the angles of a quadrilateral is 1 isto 2 isto 3 isto 4 then the measure of the smallest angle​

Answer 1

Correct Question:

• The ratio of the angles of a quadrilateral is 1 : 2 : 3 :4 then the measure of the smallest angle

Answer :

• Smallest angle is 36⁰

Given :

• The ratio of the angles of a Quadrilateral is 1:2:3:4

To find :

• Smallest angle

Solution :

Given ,

Ratio of the angles of a Quadrilateral is 1:2:3:4 then,

• Let the ratio be x , 2x , 3x and 4x

As we know that,

• Sum of all angles of Quadrilateral is 360⁰

⟶ x + 2x + 3x + 4x = 360

⟶ x + 9x = 360

⟶ 10x = 360

⟶ x = 360/10

⟶ x = 36⁰

Now , we have to find the smallest angle

• x = 36⁰
• 2x = 2(36) = 72⁰
• 3x = 3(36) = 108⁰
• 4x = 4(36) = 144⁰

Hence , Smallest angle is 36⁰

Answer 2

Given:-

• Ratio of all angles of quadrilateral = 1 : 2 : 3 : 4

To Find:-

• Measure of smallest angle

Property used:-

• Angle Sum Property :- Sum of all angles of quadrilateral is 360°

Solution:-

Let the angles be 1x , 2x , 3x and 4x.

By Angle Sum Property,

➠ 1x + 2x + 3x + 4x = 360°

➠ 10x = 360°

➠ x = 36°

Hence, the smallest angle of the given quadrilateral is x which is 36°.

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