Geometry

Question Analysis: This question is about the relative size of the vertex angle in an isosceles triangle compared to the base angles.

Key Concept Explanation:
In an isosceles triangle, the two base angles are equal.
The size of the vertex angle can vary.
While it can be larger than the base angles, it can also be equal to or smaller than the base angles.
For example, in an isosceles right triangle, the vertex angle is 90° and the base angles are each 45°, so the vertex angle is the largest.
But in an isosceles triangle with base angles of 70° each, the vertex angle is 40°, which is smaller than the base angles.

Step - by - Step Solution:
Consider the general case of an isosceles triangle with base angles x and vertex angle y.
By the angle sum property of triangles,