Understanding Isosceles Triangles: Calculating Vertex Angles

vertex angle of an isosceles triangle

In an isosceles triangle, the vertex angle is the angle formed at the vertex of the triangle where the two equal sides meet

In an isosceles triangle, the vertex angle is the angle formed at the vertex of the triangle where the two equal sides meet. This angle is also known as the base angle.

Let’s denote the vertex angle as “x”. Since an isosceles triangle has two equal sides, the base angles (or vertex angles) are also equal. Therefore, we can denote the other two base angles as “y” as well.

In an isosceles triangle, the sum of all three angles is always 180 degrees. Since the vertex angle and the base angles are equal, we can express this as:

x + y + y = 180 degrees

Simplifying this equation, we get:

x + 2y = 180 degrees

We know that the base angles are equal, so we can substitute “y” with “x” in the equation:

x + 2x = 180 degrees

Combining like terms:

3x = 180 degrees

Dividing by 3 on both sides:

x = 60 degrees

Therefore, the vertex angle (or base angle) of an isosceles triangle is equal to 60 degrees.

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