Q. 104.8( 4 Votes )

In triangle ABC, A – B = 15° and B – C = 30°, find A, B, and C.

Answer :

In a triangle ABC, it is given that


A – B = 15° and B – C = 30°


⇒ ∠A = B + 15° and C = B – 30°


We know that the sum of the angles of a triangle is 180°.


⇒ ∠A + B + C = 180°


⇒ ∠B + 15° + B + B – 30° = 180°


3B = 180° + 15°


3B = 195°


⇒ ∠B = 65°


So, A = B + 15° =65°+15° = 80°


C = B – 30°= 65°- 30° = 35°


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Karnataka Board - Mathematics Part I