Answer :

Given ΔABC, ACD = 112° and AB = AC


To find the measurement of ABC, ACB and BAC


In the given figure, BCD is a straight line, so


BCD = 180°


But, BCD = ACB + ACD


ACB + ACD = 180°


But given ACD = 112°, so the above equation becomes,


ACB + 112° = 180°


ACB = 180° - 112°


ACB = 68°………(i)


Now consider ΔABC, it is given AB = AC


We know angles opposite to equal sides are equal, therefore


⇒∠ACB = ABC


Now equation (i) in above equation we get


ABC = 68°……….(ii)


Considering the same triangle, i.e., ΔABC


We know in a triangle the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.


So in this case ACD is an exterior angle, therefore


ACD = ABC + BAC


Substituting the values from given criteria and equation (ii), we get


112° = 68° + BAC


BAC = 112° - 68°


BAC = 44°……..(iii)


Hence from equation (i), (ii) and (iii), the measurements are


ABC = 68°, ACB = 68° and BAC = 44°


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