Beam BK divides the extended angle ABC into two angles So that the degree measure of the angle ABK

Beam BK divides the extended angle ABC into two angles So that the degree measure of the angle ABK is 30 degrees less than the degree measure of the angle CBC to which the degree measures of the angles ABC and СВK are equal

Let us denote by the variable x the degree value of the angle ABK.
Therefore, according to the condition of the problem, we can represent the degree value of the СВK angle through (x + 30).
Knowing that the angles ABK and СВK together form an unfolded angle, the degree value of which, by definition, is equal to 180 °, we draw up an equation and determine the degree value of each of the indicated angles:

x + (x +30) = 180;
2x = 150;
x = 75;
180 – 75 = 105.

Answer: The degree value of the angle CBK is equal to 105 °, and the degree value of ABC is equal to 180 °.