Answer:
x = 7
Exterior angle = 139°
Step-by-step explanation:
[tex] (15x + 34) [/tex] is an exterior angle to the ∆ given.
29° and [tex] (12x + 26) [/tex] are two opposite interior angles of the ∆.
According to the external angle theorem, [tex] (15x + 34) = 29 + (12x + 26) [/tex]
Solve for x using this expression
[tex] 15x + 34 = 29 + 12x + 26 [/tex]
[tex] 15x + 34 = 29 + 26 + 12x [/tex]
[tex] 15x + 34 = 55 + 12x [/tex]
[tex] 15x + 34 - 12x = 55 + 12x - 12x [/tex]
[tex] 15x - 12x + 34 = 55 [/tex]
[tex] 3x + 34 - 34 = 55 - 34 [/tex]
[tex] 3x = 21 [/tex]
[tex] \frac{3x}{3} = \frac{21}{3} [/tex]
[tex] x = 7 [/tex]
Exterior angle = [tex] (15x + 34) [/tex]
Plug in the value of x
[tex] 15(7) + 34 = 105 + 34 = 139 [/tex]
Exterior angle = 139°
