If m∠ABC is 160°, and m∠ABD is 92°, what is the angle measure of DBC? ∠ABD and ∠DBC are adjacent angles inside ∠ABC.(1 point) Responses 92° 92 degrees 68° 68 degrees 80° 80 degrees 160°
To find the measure of angle DBC, we can use the fact that the sum of the angle measures in a triangle is 180 degrees.
Since angle ABC is 160 degrees and angle ABD is 92 degrees, we can find angle BAC by subtracting the measure of angle ABD from angle ABC:
160 degrees - 92 degrees = 68 degrees
Now, angle BAC and angle BCA together form a straight line, so their measures sum up to 180 degrees.
180 degrees - 68 degrees = 112 degrees
Therefore, angle DBC is 112 degrees.
The correct answer is 112°.