Question

In AABC, if A+ B = 125° and A+ C = 113°, then find |A, B and C.​

Answer 1

Question :

In ∆ABC , if ∠A+∠B=125° and ∠A+∠C=113° , then find ∠A , ∠B and ∠C .

Answer :

∠A = 58° , ∠B = 67° and ∠C = 55°

Solution :

• Note : Angle sum property of a triangle ; The sum of all the three interior angles of a triangle is equal to 180° .

• Given : ∠A+∠B=125°, ∠A+∠C=113°
• To find : ∠A , ∠B , ∠C = ?

We have ,

∠A + ∠B = 125° -----(1)

∠A + ∠C = 113° ------(2)

Now ,

Adding eq-(1) and (2) , we get ;

=> ∠A + ∠B +∠A + ∠C = 125° + 113°

=> ∠A + (∠A + ∠B + ∠C) = 238°

=> ∠A + 180° = 238°

=> ∠A = 238° - 180°

=> ∠A = 58°

Now ,

Using eq-(1) , we get ;

=> ∠A + ∠B = 125°

=> 58° + ∠B = 125°

=> ∠B = 125° - 58°

=> ∠B = 67°

Now ,

Using eq-(2) , we get ;

=> ∠A + ∠C = 113°

=> 58° + ∠C = 113°

=> ∠C = 113° - 58°

=> ∠C = 55°

Hence ,

∠A = 58° , ∠B = 67° and ∠C = 55° .