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 = 2∠C

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

⇒ ∠ A + 3∠C + ∠ C = 180°

⇒ ∠ A + 4∠ C – 180° = 0

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

On comparing with a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0we get,

a_{1 =} 1, b_{1} = – 2, c_{1} = 0; a_{2} = 1, b_{2} = 4, c_{2} = – 180

Applying cross multiplication method which says,

Putting the given values in the above equation we get,

Similarly,

∴ ∠ B = 3∠C = 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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