Question

The angles of quadrilateral are x - 10°, x + 10°, x and x + 20°. what will be the measure of the largest angle of the quadrilateral?

Answer 1

Given :

• Angles of quadrilateral are x - 10°, x + 10°, x and x + 20°.

To Find :

• Measure of the largest angle of Quadrilateral.

Solution :

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

$\longmapsto\tt{x{\cancel{-10}}\degree+x{\cancel{+10}}\degree+x+x+20=360\degree}$

$\longmapsto\tt{4x+20\degree=360\degree}$

$\longmapsto\tt{4x=360\degree-20\degree}$

$\longmapsto\tt{4x=340\degree}$

$\longmapsto\tt{x=\cancel\dfrac{340}{4}}$

$\longmapsto\tt\bf{x=85}$

Value of x is 85 ...

Therefore :

$\longmapsto\tt{Measure\:of\:1st\:Angle=85\degree-10\degree}$

$\longmapsto\tt\bf{75\degree}$

$\longmapsto\tt{Measure\:of\:2nd\:Angle=85\degree+10\degree}$

$\longmapsto\tt\bf{95\degree}$

$\longmapsto\tt\bf{Measure\:of\:3rd\:Angle=85\degree}$

$\longmapsto\tt{Measure\:of\:4th\:Angle=85\degree+20\degree}$

$\longmapsto\tt\bf{105\degree}$

So , The Measure of the largest angle is 105°...