Final answer:
The measure of ∠ABC can be found by recognizing that the angles ∠ABC and ∠ACB are supplementary if they are part of the same circle or cyclic quadrilateral. By using the supplementary angle property, we calculate m∠ABC to be 160º.
Step-by-step explanation:
To find the measure of ∠ABC, we need to consider the given information about the angles in the question. We're told that ∠DAB equals 110º and the measure of ∠ACB equals 20º. If we assume that points A, B, C, and D are part of a circle or a cyclic quadrilateral (since no diagram is provided, we use common geometric scenarios), angle ABC would be part of the same segment as angle ACB, and thus the two angles would be supplementary to each other as angles in a circle subtended by the same arc are supplementary.
Therefore, m∠ABC + m∠ACB = 180º (sum of supplementary angles). Plugging in the known value for ∠ACB:
m∠ABC + 20º = 180º
To find m∠ABC, we subtract 20º from both sides of the equation:
m∠ABC = 180º - 20º
Thus, m∠ABC = 160º.