Question

the four angles of a Quardileteral are in the ratio 1:2:3:4, the measure of it's smallest angle is a) 120° b) 36° c) 18° d) 10°​

Answer 1

Answer:

Step-by-step explanation:

smallest angle = 1/(1+2+3+4)* 360

= 1/10 * 360

= 36 degrees

Answer 2

Answer

• The smallest angle = 36°.

Given

• The measures of angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4.

To Find

• The smallest angle.

Step By Step Explanation

Assumption :

Let us assume that the angles of a quadrilateral are x, 2x , 3x and 4x.

Angle sum property of Quadrilateral :

Angle sum property of the quadrilateral states that the sum of all the angles of a quadrilateral = 360°.

Equation :

According to the given information equation will be ⤵

$\red \bigstar \: \: \: \: \: \: \purple{ \underline {\boxed{ \bold{x + 2x + 3x + 4x = 360}}}}$

Solution of Equation :

$\longmapsto \sf x+ 2x + 3x + 4x = 360 \\ \\ \longmapsto \sf 10x = 360 \\ \\ \longmapsto \sf x = \cfrac{ \cancel{360}}{ \cancel{10}} \\ \\ \longmapsto \underline{ \boxed{\bold{ \green{ x = 36}}}} \: \: \: \: \: \: \red\bigstar$

Now, All the angles are → 36, 72, 108 and 144.

Therefore, the smallest angle = 36°.

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