Q. 5

In AABC, the measure of B is thrice to the measure of C and the measure of A is the sum of the measures of B and C. Find the measures of all the angles of AABC and also state the type of this triangle.

Answer :

Given B = 3 C …(i)


And …(ii)


Putting (i) in (ii),



A = 2C


We know that the angle sum property of a triangle states that A + B + C = 180°


A + 3C + C = 180°


A + 4 C – 180° = 0


Consider A – 2C = 0 and A + 4 C – 180 = 0


On comparing with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0we get,


a1 = 1, b1 = – 2, c1 = 0; a2 = 1, b2 = 4, c2 = – 180


Applying cross multiplication method which says,



Putting the given values in the above equation we get,






Similarly,



B = 3C = 3× 30° = 90°


One of the angles of this triangle is 90° i.e. B


∆ABC is a right angled triangle.


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