Respuesta :

Solution:

We know that:

  • Interior angles of a triangle sum up to 180°.
  • [tex]3a + 7u + 9 = 180\°[/tex]

This means that:

  • [tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex]

Let's simplify the equation to find a.

Step-by step calculations:

Open the brackets:

  • [tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex]
  • [tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex]

Cancel same terms on both sides:

  • [tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex]
  • [tex]2a - 3 + 32 = 3a[/tex]

Simplify the LHS:

  • [tex]2a + 29 = 3a[/tex]

Subtract 2a both sides:

  • [tex]2a - 2a + 29 = 3a - 2a[/tex]
  • => [tex]29 = 3a - 2a[/tex]

Simplify the RHS and change the sides:

  • => [tex]\bold{a = 29}[/tex]

Let's substitute the value of a in 3a + 7u + 9 = 180° to find u.

  • [tex]3a + 7u + 9 = 180\°[/tex]
  • => [tex]3(29) + 7u + 9 = 180\°[/tex]

Simplify the LHS:

  • => [tex]87 + 9 + 7u = 180[/tex]
  • => [tex]96 + 7u = 180[/tex]

Subtract 96 both sides:

  • => [tex]96 - 96 + 7u = 180 - 96[/tex]
  • => [tex]7u = 84[/tex]

Divide 7 both sides:

  • => [tex]\frac{7u}{7} = \frac{84}{7}[/tex]
  • => [tex]\bold{u = 12}[/tex]

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