Answer :

(i) The given triangle with naming is as shown below:



Given ACB=55°, BAC=40°


To find the angle, i.e., ABC=x°


Now Consider the ΔABC,


We know in a triangle the sum of all three interior angles is equal to 180°.


So in this case,


ABC+BAC+ACB=180°


Substituting the values, we get


x°+40°+55°=180°


x°=180°-40°-55°


x°=85°


So the measurement of unknown angle in this triangle is 85°.


(ii) The given triangle with naming is as shown below:



Given ACB=30°, BAC=30°


To find the angle, i.e., ABC=x°


Now Consider the ΔABC,


We know in a triangle the sum of all three interior angles is equal to 180°.


So in this case,


ABC+BAC+ACB=180°


Substituting the values, we get


x°+30°+30°=180°


x°=180°-30°-30°


x°=120°


So the measurement of unknown angle in this triangle is 120°.


(iii) The given triangle with naming is as shown below:



Given triangle is a right-angled triangle, so ABC=90° and also given ACB=30°


To find the angle, i.e., BAC=x°


Now Consider the ΔABC,


We know in a triangle the sum of all three interior angles is equal to 180°.


So in this case,


ABC+BAC+ACB=180°


Substituting the values, we get


90°+x°+30°=180°


x°=180°-90°-30°


x°=60°


So the measurement of unknown angle in this triangle is 60°.


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