Answer:
k = 10°
Step-by-step explanation:
[tex] {115}^{o} = {(4k + 5)}^{o} + {(6k + 10)}^{o} \\ [/tex]
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
[tex] {115}^{o} = {(4k + 5)}^{o} + {(6k + 10)}^{o} \\ {115}^{o} = 4k + 5 + 6k + 10 \\ {115}^{o} = 10k + 15 \\ {115}^{o} - 15 = 10k \\ {100}^{o} = 10k \\ \frac{100}{10} = k \\ {10}^{o} = k \\ [/tex]
