Question

Solve for the exterior angle in the image below?

Answer 1

x = 7

Exterior angle = 139°

Explanation:

`(15x + 34)` is an exterior angle to the ∆ given.

29° and
`(12x + 26)` are two opposite interior angles of the ∆.

According to the external angle theorem,
`(15x + 34) = 29 + (12x + 26)`

Solve for x using this expression

`15x + 34 = 29 + 12x + 26`

`15x + 34 = 29 + 26 + 12x`

`15x + 34 = 55 + 12x`

`15x + 34 - 12x = 55 + 12x - 12x`

`15x - 12x + 34 = 55`

`3x + 34 - 34 = 55 - 34`

`3x = 21`

`(3x)/(3) = (21)/(3)`

`x = 7`

Exterior angle =
`(15x + 34)`

Plug in the value of x

`15(7) + 34 = 105 + 34 = 139`

Exterior angle = 139°