M∆abc=17x+8, m∆abk=42°, and m∆kbc=12x-4. Find m∆abc

So, we have as a given that:

measure angle ABK + measure angle KBC = measure angle ABC

Substitute with the givens and solve for x first.

42 + 12x - 4 = 17x + 8

42 - 4 - 8 = 17x - 12x

30 = 5x

x = 30/5 = 6

Therefore:

measure angle ABC = 17x + 8 = 17 (6) + 8 = 110 degrees