Question

What will be the measure of smallest angle of a quadrilateral if the ratio of the four angle 1:2:3:4

Answer 1

given ratio = 1 : 2 : 3 : 4

let angles be x , 2x , 3x and 4x

sum of the angles of quadrilateral = 360°

x + 2x + 3x + 4x = 180°

10x = 180°

$\fcolorbox{red}{yellow}{x\:=\:18°}$

first angle = x = $\bold\pink{18°}$

second angle = 2x = 2 × 18° = $\bold\blue{36°}$

third angle = 3x = 3 × 18° = $\bold\green{54°}$

fourth angle = 4x = 4 × 18° = $\bold\orange{72°}$

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Answer 2

Answer :-

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

• Sum of all angles of quadrilateral = 360°

x + 2x + 3x + 4x = 360°

10x = 360°

x = 36°

Angles = 36° , 72° , 108° and 144°

Smallest angle = 36°