Question

If the measures of the angles of a quadrilateral are (3x+15)Degrees,(x+20)degrees, (2x+30) degrees, and (3x-20)degree,then the difference between the greatest and the smallest angel of the given quadrilateral is

Answer 1

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Answer 2

The difference between the greatest and the smallest angle of the given quadrilateral is 65°

Step-by-step explanation:

The angles of quadrilateral are:

Angle 1 = $(3x+15)^{\circ}$

Angle 2 = $(x+20)^{\circ}$

Angle 3 = $(2x+30)^{\circ}$

Angle 4 = $(3x-20)^{\circ}$

Sum of all angles of quadrilateral = 360 °

So, 3x+15+x+20+2x+30+3x-20= 360

3x+15+x+20+2x+30+3x-20= 360

9x+45=360

9x=360-45

9x=315

$x=\frac{315}{9}$

x=35

Angle 1 =$(3x+15)^{\circ}=3(35)+15=120^{\circ}$

Angle 2 = $(x+20)^{\circ}=35+20=55^{\circ}$

Angle 3=$(2x+30)^{\circ}=(2(35)+30)=100^{\circ}$

Angle 4 =$(3x-20)^{\circ}=(3(35)-20)=85^{\circ}$

Difference between the he greatest and the smallest angle = 120-55= 65

Hence the difference between the greatest and the smallest angle of the given quadrilateral is 65°

#Learn more:

The angles of a quadrilateral are xdegree, x-10 degree,x+52and 3x find the greatest angel

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