Q. 164.2( 5 Votes )

In an isosceles triangle, the vertex angle is twice the sum of the base angles. Find the angles of the triangle.

Answer :

In a triangle ABC, let A be the vertex angle and C and B be the base angles. It is given that


B = C { it is an isosceles triangle}


And A = 2(B + C)


⇒ ∠A = 2× 2 B


A = 4 B


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


4B + B + B = 180°


6B = 180 °


⇒ ∠B = 30°


So, C = B = 30°


And A = 4× B = 120°


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In a triangle ABC, B = 70°. Find A + C.

Karnataka Board - Mathematics Part I