Question

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

Answer 1

We know that in an isosceles triangle the two base angles are equal so let's get the sum of both
54+54 = 108
So the vertex angle equals
180-108
72°

Answer 2

72
`\degree`

Explanation:

We know that the sum of all the angles of any triangle is 180
`\degree`

We have to use the above property in order to find the measurement of the vertex angle.

Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54
`\degree`

And hence the other will also be 54
`\degree`.

Let the vertex angle be x

180=54+54+×

180=108+×

x=180-108

x=72

Hence the vertex angle is 72
`\degree`