How do I find the base angles of an isosceles triangle?

Subtract the vertex angle from 180° to get the sum of the two base angles, then divide by 2. For example, if the vertex angle is 40°, each base angle is (180 - 40) / 2 = 70°.

What is the formula for the base angle of an isosceles triangle?

Base angle = (180° - vertex angle) / 2. This works because the sum of all angles in any triangle is 180°, and in an isosceles triangle the two base angles are equal.

Can I use this calculator for any vertex angle?

Yes, as long as the vertex angle is between 0° and 180°. If you enter a value outside this range, the calculator will not produce a valid triangle.

Math

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Isosceles Triangle Angles Calculator.

Find the two equal base angles from the vertex angle.

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Set your values

Results update as you type.

02 / ANSWER

Vertex angle

40°

Base angle

70°

Angle sum

180°

Results update automatically as you type.

Use Cases

Geometry homework and exam prep

Quickly verify your manual calculations for isosceles triangle base angles, saving time and reducing errors.

Example: Check that a vertex angle of 50° gives base angles of 65° each.

Design and construction planning

Determine the angles for roof trusses, gables, or other symmetrical structures that use isosceles triangles.

Example: For a roof with a 30° peak, each base angle is 75°.

Frequently Asked Questions

How do I find the base angles of an isosceles triangle?: Subtract the vertex angle from 180° to get the sum of the two base angles, then divide by 2. For example, if the vertex angle is 40°, each base angle is (180 - 40) / 2 = 70°.
What is the formula for the base angle of an isosceles triangle?: Base angle = (180° - vertex angle) / 2. This works because the sum of all angles in any triangle is 180°, and in an isosceles triangle the two base angles are equal.
Can I use this calculator for any vertex angle?: Yes, as long as the vertex angle is between 0° and 180°. If you enter a value outside this range, the calculator will not produce a valid triangle.

Tips & Common Mistakes

Tips

Remember that the sum of all angles in a triangle is always 180°. Use this to check your result.
If you know the base angles instead, you can find the vertex angle by subtracting twice the base angle from 180°.
For a quick mental check, the base angles are always less than 90° because the vertex angle is positive.
Use the calculator for any vertex angle between 0° and 180°; outside this range, a triangle cannot exist.

Common Mistakes to Avoid

Forgetting to divide by 2 after subtracting the vertex angle from 180°. The sum of the two base angles must be split equally.
Entering a vertex angle greater than or equal to 180°, which would make the base angles zero or negative, an impossible triangle.
Assuming the base angles are equal to the vertex angle; they are only equal in an equilateral triangle (vertex angle = 60°).

Last updated: August 13, 2026