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.

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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