Final answer:
The correct answers are m∡KBC = 28.3° and m∡ABC = 56.6°, as BK bisects ∡ABC creating two congruent angles. The sum of these angles gives the measurement of ∡ABC.
Step-by-step explanation:
The question involves determining the measurements of angles when a line bisects another angle. Given that BK bisects ∡ABC and m∡ABK = 28.3°, we can conclude that BK divides ∡ABC into two equal parts. Therefore, m∡KBC must also be 28.3°, because bisectors create two congruent angles. To find m∡ABC, we simply add the measures of the two adjacent angles ABK and KBC. The sum is 28.3° + 28.3° = 56.6°.
Thus, the correct answer is:
m∡KBC = 28.3°, m∡ABC = 56.6°.
The corresponding option based on the given set of multiple-choice answers is A. m∡KBC = 28.3°, m∡ABC = 56.6°.