Question

Can someone help me with this question please!!!!!

Answer 1

We know that:

• Interior angles of a triangle sum up to 180°.
• 
  `3a + 7u + 9 = 180\°`

This means that:

• 
  `(7u + 9) + (2a - 3) + 32 = 3a + 7u + 9`

Let's simplify the equation to find a.

Step-by step calculations:

Open the brackets:

• 
  `(7u + 9) + (2a - 3) + 32 = 3a + 7u + 9`
• 
  `7u + 9 + 2a - 3 + 32 = 3a + 7u + 9`

Cancel same terms on both sides:

• 
  `7u + 9 + 2a - 3 + 32 = 3a + 7u + 9`
• 
  `2a - 3 + 32 = 3a`

Simplify the LHS:

• 
  `2a + 29 = 3a`

Subtract 2a both sides:

• 
  `2a - 2a + 29 = 3a - 2a`
• =>
  `29 = 3a - 2a`

Simplify the RHS and change the sides:

• =>
  `\bold{a = 29}`

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

• 
  `3a + 7u + 9 = 180\°`
• =>
  `3(29) + 7u + 9 = 180\°`

Simplify the LHS:

• =>
  `87 + 9 + 7u = 180`
• =>
  `96 + 7u = 180`

Subtract 96 both sides:

• =>
  `96 - 96 + 7u = 180 - 96`
• =>
  `7u = 84`

Divide 7 both sides:

• =>
  `(7u)/(7) = (84)/(7)`
• =>
  `\bold{u = 12}`