Question

The measure of the vertex angle of an isosceles triangle is three times the measure of a base angle. Find the number of degrees in the measure of the vertex angle.

Answer 1

We will label the base angles of the triangle as "x".

`\text{Base angle=x}`

Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:

`\text{Vertex angle =3x}`

The following image represent the angles in the isosceles triangle:

Now we use the following property of triangles:

The sum of all of the internal angles in a triangle must be equal to 180°.

Thus, we add the angles and equal them to 180°

`3x+x+x=180`

We combine the terms on the left:

`5x=180`

And divide both sides by 5:

`\begin{gathered} (5x)/(5)=(180)/(5) \\ x=36 \end{gathered}`

And since x=36, the vertex angle will be:

`\text{vertex angle = 3x = 3(36)=108\degree}`

answer: 108°