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Write and solve an equation to find the value of x.

1/3x °
(x-20)°
(x-10)°
40°

Sum of angle measures: 360°

Write and solve an equation to find the value of x 13x x20 x10 40 Sum of angle measures 360 class=

Respuesta :

Viserion

Answer:

→ 150°

Step-by-step explanation:

In this question, we are provided with a quadrilateral whose angles are as given below :

  • [tex] \sf{\dfrac{1}{3}x° }[/tex]

  • [tex] \sf{(x - 10)°}[/tex]

  • [tex] \sf{40°}[/tex]

  • [tex] \sf{(x - 20)°}[/tex]

We need to find the value of x.

Solution:

As we know that , sum of all the four angles of Quadrilateral is equal to 360°. So we are adding all the angles and equating it with 360° to form an equation. And after solving it for x , we can easily get the value of x.

Equation Formed :

[tex] \sf{ \dashrightarrow \: \dfrac{1}{3} x + (x - 10) + 40 + (x - 20) = 360}[/tex]

Solving Equation:

[tex]\sf{ \dashrightarrow \: \dfrac{1}{3} x + x - 10+ 40 + x - 20 = 360}[/tex]

[tex]\sf{ \dashrightarrow \: \dfrac{1}{3} x + 2x + 10 \: \: \: = 360}[/tex]

[tex]\sf{ \dashrightarrow \: \dfrac{1x + 6x}{3} \: \: \: = 360 - 10}[/tex]

[tex]\sf{ \dashrightarrow \: \dfrac{7x}{3} \: \: \: = 350}[/tex]

[tex]\sf{ \dashrightarrow \: 7x \: \: \: = 1050}[/tex]

[tex]\sf{ \dashrightarrow \: x \: \: \: = \dfrac{1050}{7}}[/tex]

[tex]\sf{ \dashrightarrow \: \underline{ \boxed{\bold{ x \: \: \: = 150°}}}} \: \: \: \bigstar[/tex]

>>> Therefore, value of x is 150°.

msm555

Answer:

[tex]\sf x = 150[/tex]

Step-by-step explanation:

To find the value of [tex]\sf x [/tex], we can set up an equation based on the sum of the angle measures in a quadrilateral, which is [tex]\sf 360^\circ [/tex].

Given angles:

  • [tex]\sf \dfrac{1}{3}x [/tex]
  • [tex]\sf (x - 20)^\circ [/tex]
  • [tex]\sf (x - 10)^\circ [/tex]
  • [tex]\sf 40^\circ [/tex]

The sum of these angles must be [tex]\sf 360^\circ [/tex].

So, we can write the equation:

[tex]\sf \dfrac{1}{3}x + (x - 20) + (x - 10) + 40 = 360 [/tex]

Now, let's solve for [tex]\sf x [/tex]:

[tex]\sf \dfrac{1}{3}x + x - 20 + x - 10 + 40 = 360 [/tex]

Combine like terms:

[tex]\sf \dfrac{1}{3}x + 2x - 30 + 40 = 360 [/tex]

[tex]\sf \dfrac{1}{3}x + 2x + 10 = 360 [/tex]

Subtract 10 from both sides:

[tex]\sf \dfrac{1}{3}x + 2x + 10 -10 = 360 -10 [/tex]

[tex]\sf \dfrac{1}{3}x + 2x = 350 [/tex]

Multiply both sides by 3.

[tex]\sf \dfrac{1}{3}x \cdot 3 + 2x \cdot 3 = 350 \cdot 3 [/tex]

[tex] \sf x + 6x = 1050[/tex]

[tex]\sf 7x = 1050 [/tex]

Divide both sides by 7:

[tex]\sf x = \dfrac{1050}{7} [/tex]

[tex]\sf x = 150 [/tex]

So, the value of [tex]\sf x [/tex] is 150.

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