Question

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

Answer 1

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