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

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11
Nov 14, 2015

${90}^{\circ}$

#### Explanation:

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

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Veddesh Share
Jan 9, 2018

${90}^{\circ}$

#### 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 $2 x$ (since it is twice the base angle)

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

So,

$\rightarrow 2 x + x + x = {180}^{\circ}$

$\rightarrow 4 x = {180}^{\circ}$

$\rightarrow x = \frac{180}{4}$

color(green)(rArrx=45^circ

Now the other angle is $2 x$ which is $45 \times 2 = {90}^{\circ}$

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

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