In an isosceles triangle, the vertex angle is four times the sum of the base angles. The measure of the square root of the vertex angle is:

Correct option is D

Given:
In isosceles triangle, vertex angle is four times the sum of base angles.
Formula Used:
Angle sum property of a triangle = $$180^°$$​​
Solution:
As per the property of isosceles triangle, two of the sides will be same.
So, let the base angles be x and x.
Vertex angle = 4 × Sum of base angles
Vertex angle = 4 × (x + x) = 8x
As per angle sum property of a triangle,
8x + x + x = 180$$^°$$​
10x = 180$$^°$$​
x = 180/10=18$$^°$$​​
Vertex angle = 8x = 8 × 18$$^°$$​ = 144$$^°$$​
Square root of vertex angle = √144=12$$^°$$​​