Question

In an isosceles triangle, the vertex angle is twice the each base angle. What is the vertex angle?

Answer 1

`90^@`

Explanation:

Since the sum of the interior angles of any triangle adds up to `180^@` and also the base angles of an isosceles triangle are equal,we may let the base angles be `x`, then the vertex angle is `2x`.
`therefore x+x+2x=180^@`.
`therefore x=45^@`.
Therefore the vertex angle is `90^@`.

Answer 2

`90^circ`

Explanation:

An isosceles triangle has two sides of equal length. Likewise, the opposite angles of the sides are the same

So lets assume each angle be `x` and the bigger angle be `2x` (since it is twice the base angle)

Now, we know that sum of the angles in a triangle is 180 degree

So,

`rarr2x+x+x=180^circ`

`rarr4x=180^circ`

`rarrx=180/4`

`color(green)(rArrx=45^circ`

Now the other angle is `2x` which is `45xx2=90^circ`

Hope this helps!!! ☺☻ have a good day...