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

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1 Answer
bepri
Nov 12, 2017

#m/_ABC=70#

Explanation:

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

Once we've found the measure of #/_BAC# to be 75°, and given the measure of #/_ACB# to be 35, we can then find the measurement of #/_ABC#.

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=180#
#110+m/_ABC=180#
#m/_ABC=70#

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