Respuesta :

Answer:

Given:

A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x

To find :

The value of angle 7x+6

Solution:

we know that ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.

so,

[tex]7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10[/tex]

so ,the measure of green angle would be

[tex]7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76[/tex]

Verification:

To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)

so,

[tex]7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified[/tex]

Solution:

Note that:

  • Green angle = 7x + 6
  • 4x + 7x + 6 + (180 - 116) = 180

Simplify the equation to find x.

  • 4x + 7x + 6 + (180 - 116) = 180
  • => 11x + 6 + (64) = 180
  • => 11x + 70 = 180
  • => 11x = 180 - 70
  • => 11x = 110
  • => x = 110/11 = 10

Substitute the value of x into the measure of the green angle.

  • 7x + 6
  • => 7(10) + 6
  • => 76°

The measure of the green angle is 76°.

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