Question

The angle of a quadrilateral are (5x)°,5(x+2)°,(6x-20)° and 6(x+3)°respectiply. Find the value of x and each angle of the quadrilateral.

Answer 1

★ Solution :-

We know that, each 2-D shape has an angle sum property. For a quadrilateral also, we have an angle sum property. So, using this concept we can find the answer of this question. The angle sum property of a quadrilateral says that, all angles in a triangle measures upto 360°. So,

$\sf \longrightarrow Angle \: sum \: property_{(Quadrilateral)} = {360}^{\circ}$

$\sf \longrightarrow (5x) + 5(x + 2) + (6x - 20) + 6(x + 3) = {360}^{\circ}$

$\sf \longrightarrow (5x) + (5x + 10) + (6x - 20) + (6x + 18) = {360}^{\circ}$

$\sf \longrightarrow 5x + 5x + 6x + 6x + 10 - 20 + 18 = {360}^{\circ}$

$\sf \longrightarrow 22x + 8 = {360}^{\circ}$

$\sf \longrightarrow 22x = 360 - 8$

$\sf \longrightarrow 22x = 352$

$\sf \longrightarrow x = \dfrac{352}{22}$

$\sf \longrightarrow x = 16$

Now, we can find the measure of each angles.

Measure of 5x :-

$\sf \longrightarrow 5x = 5(16)$

$\sf \longrightarrow 5x = {80}^{\circ}$

Measure of 5(x+2) :-

$\sf \longrightarrow 5(x + 2) = 5(16 + 2)$

$\sf \longrightarrow 5(x + 2) = 5(18)$

$\sf \longrightarrow 5(x + 2) = {90}^{\circ}$

Measure of 6x-20 :-

$\sf \longrightarrow 6x - 20 = 6(16) - 20$

$\sf \longrightarrow 6x - 20 = 96 - 20$

$\sf \longrightarrow 6x - 20 = {76}^{\circ}$

Measure of 6(x+3) :-

$\sf \longrightarrow 6(x + 3) = 6(16 + 3)$

$\sf \longrightarrow 6(x + 3) = 6(19)$

$\sf \longrightarrow 6(x + 3) = {114}^{\circ}$

Hence, solved !!

Answer 2

Step-by-step explanation:

Solution :-

We know that, each 2-D shape has an angle sum property. For a quadrilateral also, we have an angle sum property. So, using this concept we can find the answer of this question. The angle sum property of a quadrilateral says that, all angles in a triangle measures upto 360°. So,

\sf \longrightarrow Angle \: sum \: property_{(Quadrilateral)} = {360}^{\circ}⟶Anglesumproperty

(Quadrilateral)

=360

∘

\sf \longrightarrow (5x) + 5(x + 2) + (6x - 20) + 6(x + 3) = {360}^{\circ}⟶(5x)+5(x+2)+(6x−20)+6(x+3)=360

∘

\sf \longrightarrow (5x) + (5x + 10) + (6x - 20) + (6x + 18) = {360}^{\circ}⟶(5x)+(5x+10)+(6x−20)+(6x+18)=360

∘

\sf \longrightarrow 5x + 5x + 6x + 6x + 10 - 20 + 18 = {360}^{\circ}⟶5x+5x+6x+6x+10−20+18=360

∘

\sf \longrightarrow 22x + 8 = {360}^{\circ}⟶22x+8=360

∘

\sf \longrightarrow 22x = 360 - 8⟶22x=360−8

\sf \longrightarrow 22x = 352⟶22x=352

\sf \longrightarrow x = \dfrac{352}{22}⟶x=

22

352

\sf \longrightarrow x = 16⟶x=16

Now, we can find the measure of each angles.

Measure of 5x :-

\sf \longrightarrow 5x = 5(16)⟶5x=5(16)

\sf \longrightarrow 5x = {80}^{\circ}⟶5x=80

∘

Measure of 5(x+2) :-

\sf \longrightarrow 5(x + 2) = 5(16 + 2)⟶5(x+2)=5(16+2)

\sf \longrightarrow 5(x + 2) = 5(18)⟶5(x+2)=5(18)

\sf \longrightarrow 5(x + 2) = {90}^{\circ}⟶5(x+2)=90

∘

Measure of 6x-20 :-

\sf \longrightarrow 6x - 20 = 6(16) - 20⟶6x−20=6(16)−20

\sf \longrightarrow 6x - 20 = 96 - 20⟶6x−20=96−20

\sf \longrightarrow 6x - 20 = {76}^{\circ}⟶6x−20=76

∘

Measure of 6(x+3) :-

\sf \longrightarrow 6(x + 3) = 6(16 + 3)⟶6(x+3)=6(16+3)

\sf \longrightarrow 6(x + 3) = 6(19)⟶6(x+3)=6(19)

\sf \longrightarrow 6(x + 3) = {114}^{\circ}⟶6(x+3)=114

∘

Hence, solved !!