Question

The ratio of the measure of the vertex angle is to the base angle of an isosceles triangle is $8:5$. Find the measure do the vertex angle?

Answer 1

Finding the measure of vertex angle of an isosceles triangle:

Given that ratio of the measure of the vertex angle to the base angle of an isosceles triangle is $8:5$.

We know that in isosceles triangle bases angles are equal.

So, let base angles are $5x$ and the vertex angle is $8x$ where $x$ is some integer.

We know that sum of interior angles of a triangle is $=180°$

$$\begin{gathered} \therefore 8x+5x+5x=180 \\ \Rightarrow 18x=180 \\ \Rightarrow x=10 \end{gathered}$$

$\therefore$ The vertex angle $8x=8\times 10=80°$.

Hence, the value of vertex angle is $80°$.