Answer:
x=20°
Step-by-step explanation:
Given that , an isosceles triangle, has the ratio of the measure of the vertex to the measure of a base angle is 1:4, we want to find the measure of the vertex angle.
Note that the base angles of an isosceles triangle are equal.
Therefore if the vertex angle is x, then the base angles are:
4x each
The sum of angles in a triangle is 180°
[tex]x + 4x + 4x = 180[/tex]
[tex]9x = 180[/tex]
[tex]x = \frac{180}{9} = 20[/tex]
The vertex angle is 20°
