Question

5.
In a AABC, if B=5 C and A = 3|C, then find the angles of the triangle.
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Answer 1

Question :

In a ∆ABC , if ∠B = 5∠C and ∠A = 3∠C , then find the angles of the triangle .

Answer :

∠A = 60° , ∠B = 100° and ∠C = 20°

Solution :

• Note : Angle sum property of a triangle ; The sum of all the three interior angles of a triangle is equal to 180° .
• Given : ∠B = 5∠C , ∠A = 3∠C
• To find : ∠A , ∠B , ∠C = ?

We have ,

∠B = 5∠C ------(1)

∠A = 3∠C ------(2)

Also ,

We know that , in ∆ABC ;

=> ∠A + ∠B + ∠C = 180°

[ Angle sum property of a triangle ]

=> 3∠C + 5∠C + ∠C = 180°

[ Using eq-(1) and (2) ]

=> 9∠C = 180°

=> ∠C = 180°/9

=> ∠C = 20°

Now ,

Using eq-(1) , we have ;

=> ∠B = 5×20°

=> ∠B = 100°

Now ,

Using eq-(2) , we have ;

=> ∠A = 3∠C

=> ∠A = 3×20°

=> ∠A = 60°

Hence ,

∠A = 60° , ∠B = 100° and ∠C = 20° .