The measure of ∠DAB equals 105º. The measure of ∠ACB equals 35º. What is m∠ABC?

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1 Answer
Nov 12, 2017

m/_ABC=70mABC=70

Explanation:

Given bar (DAC)¯¯¯¯¯¯¯¯¯DAC is a straight line, we can say its full measurement is 180°. If we know a segment of this angle, /_DABDAB, is 105°, we can know that the other segment /_BACBAC must equal 75, since 105+75=180105+75=180.

Once we've found the measure of /_BACBAC to be 75°, and given the measure of /_ACBACB to be 35, we can then find the measurement of /_ABCABC.

Since we know that the sum of any triangle's angles is 180°, we can then use these known measurements as I said above.

75+35+m/_ABC=18075+35+mABC=180
110+m/_ABC=180110+mABC=180
m/_ABC=70mABC=70