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Answer :
Final answer:
By applying the exterior angle theorem and the knowledge that angles on a straight line add up to 180 degrees, angle ABC in the given triangle can be computed as 78 degrees.
Explanation:
In this triangle ABC, we are given that the measure of angle CBD is 16 degrees and the measure of angle ACB is 118 degrees. We need to find the measure of angle ABC. Now, note that ABC is an exterior angle for the triangle CBD, and according to the exterior angle theorem, an exterior angle of a triangle is equal to the sum of the two remote interior angles. Therefore, angle ABC (exterior angle) = angle CBD + angle BCD.
But angle CBD is given as 16 degrees. Let's find angle BCD now. Triangle ABC is also a straight line at point C, we know that the angles on a straight line add up to 180 degrees. Thus, angle ACB (given as 118 degrees) + angle BCD = 180 degrees. Solving, we get angle BCD = 62 degrees.
Hence, angle ABC = angle CBD + angle BCD = 16 degrees + 62 degrees = 78 degrees.
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