Hey there!
In an isosceles triangle, the top angle is called the vertex angle and the two angles present at the bottom are the base angles.
Of course, the word "base" gives us the prompt that they are at the bottom.
Now, the ratio is given as 5:2 , '5' is the vertex angle and '2' is the base angle.
Now, most people get confused with the base angle. '2' is the base angle and now, people get confused with which angle to take the ratio.
But, remember, the measure of the angels on the base are equal. ( Both the base angles have the same measurement ).
This is always true for a isosceles.
Given ratio,
... 5:2
Let's take the angles as 5x and 2x.
Remember that the sum of all angles in any triangles is 180°
Hence,
... 5x + 2x + 2x = 180
This is because, there are three angles in total and the base angles are equal.
... 5x + 4x = 180
... 9x = 180
... x = 180 / 9
... x = 20
The vertex angle = 5x
... 5 ( 20 )
... 100
Hence, the measure of the vertex angle is 100°
Hope my answer helps!