Vertex Angle — Definition, Formula & Examples
Vertex angle is the angle formed at the vertex of a shape, most commonly referring to the angle between the two equal sides (legs) of an isosceles triangle.
In an isosceles triangle, the vertex angle is the angle included between the two congruent sides, opposite the base. More generally, a vertex angle is any angle formed at a vertex of a polygon by its two adjacent sides.
How It Works
In an isosceles triangle, the two sides of equal length meet at a point called the apex. The angle they form there is the vertex angle. The other two angles, located at each end of the base, are called base angles and are always equal to each other. If you know the vertex angle, you can find each base angle using the fact that all three angles sum to .
Worked Example
Problem: An isosceles triangle has a vertex angle of 40°. Find the measure of each base angle.
Step 1: The three angles of any triangle add up to 180°. Subtract the vertex angle from 180°.
Step 2: The two base angles are equal, so divide the remaining degrees by 2.
Answer: Each base angle measures 70°.
Why It Matters
Identifying the vertex angle is essential when solving problems involving isosceles and equilateral triangles, which appear frequently in middle-school geometry and standardized tests. Architects and engineers also rely on vertex angles when designing structures with symmetrical triangular supports.
Common Mistakes
Mistake: Confusing the vertex angle with one of the base angles in an isosceles triangle.
Correction: The vertex angle is always the one between the two equal sides. The base angles are the two equal angles at either end of the base.