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.

Question

asked Jul 22, 2023 216k views

1 Answer

Lilly · Answer 1 · 2023-07-29T10:32:29+0000

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°

We combine the terms on the left:

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°