Question

In a quadrilatonal ABCD, the angles
LA, LB, LC & LD are in the ratio 1:2:3:4
Find the measure of each angle of
the quadalatonal​

Answer 1

Given :

• ∠A , ∠B , ∠C , ∠D are in the ratio 1:2:3:4

To Find :

• Measure of each angle of Quadrilateral.

Solution :

$\longmapsto\tt{Let\:\angle{A}=1x}$

$\longmapsto\tt{Let\:\angle{B}=2x}$

$\longmapsto\tt{Let\:\angle{C}=3x}$

$\longmapsto\tt{Let\:\angle{D}=4x}$

Now ,

As we know that Sum of all angles of a quarilateral is 360° . So ,

$\longmapsto\tt{\angle{A}+\angle{B}+\angle{C}+\angle{D}=360\degree}$

$\longmapsto\tt{1x+2x+3x+4x=360\degree}$

$\longmapsto\tt{10x=360\degree}$

$\longmapsto\tt{x=\cancel\dfrac{360}{10}}$

$\longmapsto\tt\bf{x=36\degree}$

So , The Value of x is 36°..

Therefore :

$\longmapsto\tt{Measure\:of\:\angle{A}=1(36)}$

$\longmapsto\tt\bf{36\degree}$

$\longmapsto\tt{Measure\:of\:\angle{B}=2(36)}$

$\longmapsto\tt\bf{82\degree}$

$\longmapsto\tt{Measure\:of\:\angle{C}=3(36)}$

$\longmapsto\tt\bf{108\degree}$

$\longmapsto\tt{Measure\:of\:\angle{D}=4(36})$

$\longmapsto\tt\bf{144\degree}$

Answer 2

Answer:

Given :

∠A , ∠B , ∠C , ∠D are in the ratio 1:2:3:4

To Find :

Measure of each angle of Quadrilateral.

Solution :

$\red{\longmapsto\tt{Let\:\angle{A}=1x}}$

$\pink{\longmapsto\tt{Let\:\angle{B}=2x}}$

$\longmapsto\tt{Let\:\angle{C}=3x}$

$\blue{\longmapsto\tt{Let\:\angle{D}=4x}}</p><p>$

Now ,

As we know that Sum of all angles of a quarilateral is 360° . So ,

$\pink{\longmapsto\tt{\angle{A}+\angle{B}+\angle{C}+\angle{D}=360\degree}}$

$\green{\longmapsto\tt{1x+2x+3x+4x=360\degree}}$

$\gray{\longmapsto\tt{10x=360\degree}}</p><p>$

$\red{\longmapsto\tt{x=\cancel\dfrac{360}{10}}}$

$\orange{\longmapsto\tt\bf{x=36\degree}}$

So , The Value of x is 36°..

Therefore :

$\longmapsto\tt{Measure\:of\:\angle{A}=1(36)}</p><p>$

$\longmapsto\tt\bf{36\degree}$

$\longmapsto\tt{Measure\:of\:\angle{B}=2(36)}$

$\orange{\longmapsto\tt\bf{82\degree}}$

$\red{\longmapsto\tt{Measure\:of\:\angle{C}=3(36)}}$

$\pink{\longmapsto\tt\bf{108\degree}}$

$</p><p> \green{\longmapsto\tt{Measure\:of\:\angle{D}=4(36}}$

$\red{\longmapsto\tt\bf{144\degree}}</p><p>$

$\huge \rm \pink{Hence \: done !!}$