In an isosceles triangle, the ratio of the measure of the base angel to the vertex angle is 2:1, what is the measure of the vertex angle?

Answer 1

Vertex is angle "α".

As for a "base angle" all I can think of is angle "γ" which is opposite of side "c".

You're not giving features of a triangle.

side "a" shortest

"b" mid length

"c" hypotenuse

angles "α" opposite side "a"

"β" "b"

"γ" "c"

Please get back to me.

Answer 2

Start by writing down what you know first:

Let A, B and C be the angles of your isosceles triangle. Since this triangle is isosceles two angles have the same measure, let say B and C, so m(B)=m(C)

It also say that the ratio between vertex, or angle A and angle from base is 2:1 which means that m(A)/m(B)=2/1. This translate further into m(A)=2m(B).

To put all these given information together we need one additional property of any triangle: the sum of measure of angles is 180.

m(A)+m(B)+m(C)=180

let's ignore m for now

2B+B+B=180

4B=180

B=45

Lastly, we calculate A=2x45=90