Question

In an isosceles triangle, the base angles are equal. The vertex angle is ${{40}^{0}}$. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is ${{180}^{0}}$ )

Answer 1

Hint: In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

Complete step by step answer:
Let x be the base angle of an isosceles triangle.
It is given that the base angles of an isosceles triangle are equal and the vertex angle of an isosceles triangle is ${{40}^{0}}$ .
We know that the sum of three angles of a triangle is 180 degrees.
x + x + 40 = 180
2x + 40 = 180
2x = 180-40
2x = 140
Dividing both sides by 2, we get
x = 70.
Hence the base angle of an isosceles triangle is 70 degree.
Both the base angles are equal; the second base angle of the isosceles triangle is also 70 degree.
Therefore, the base angles of the isosceles triangle are ${{70}^{0}}$,${{70}^{0}}$.

Note: In an isosceles triangle the base angles are equal and the vertex angle is 40 degree then base angles are $\dfrac{140}{2}=70$ degree each. The name isosceles derives from the Greek iso (same) and skelos (leg).