Last updated: July 31, 2026
Isosceles Triangle Angles Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
If V is known, B=(180-V)/2; if B is known, V=180-2B; angleSum=180
Where:
- V=vertex angle(degrees)
- B=base angle(degrees)
Worked Examples
From vertex angle
Given V=50°, split the remaining 130° equally.
- 1B=(180-50)/2
- 2B=65
From base angle
Given B=70°, subtract both base angles from 180°.
- 1V=180-2×70
- 2V=40
Acute apex example
A narrow apex creates large base angles.
- 1B=(180-24)/2
- 2B=78
Invalid base angle
A base angle of 90° or more cannot form a valid isosceles triangle.
- 1Check 0<B<90
- 290 is not allowed because the vertex angle would be zero or negative.
Introduction
This isosceles triangle angles calculator finds the missing angles when you know either the vertex angle or one base angle. Because the base angles are always equal, only one angle measurement is needed to solve the full set. The result also shows the 180-degree angle sum as a quick verification.
Two ways to solve the triangle
You can start from the apex angle or from one of the two equal base angles.
- Mode 1:
enter the vertex angle V
- Mode 2:
enter one base angle B
The calculator returns both angle types in either mode
Why the base angles are equal
An isosceles triangle has two equal sides, and equal sides in a triangle stand opposite equal angles.
Equal legs imply equal base angles
Only one angle needs to be entered
The angle sum property finishes the problem
Using the vertex-angle formula
If you know the apex angle V, subtract it from 180° and divide the remainder by two.
Compute 180−V
Split the remainder equally
Each half is a base angle
This mode is useful when a drawing labels the angle at the top.
Using the base-angle formula
If you know one base angle B, subtract twice that angle from 180° to get the vertex angle.
Double the base angle
Subtract from 180°
Keep the original base angle as the repeated value
Validation rules
The calculator rejects angle values that would produce a flat or impossible triangle.
For vertex mode, 0<V<180
For base mode, 0<B<90
Mode must be fromVertex or fromBase
A base angle of exactly 90° would force the vertex angle to 0°, which is not a triangle.
Useful applications
Angle solving is useful in geometry class, drafting, roof layouts, and quick checks on symmetric designs.
Homework verification
Survey sketches
Symmetric design layouts
Triangle proof practice
FAQs
What inputs does this angle calculator need?
It needs either the vertex angle or one base angle, plus the mode that tells the calculator which value you entered.
Why are the base angles equal?
Because an isosceles triangle has two equal sides, and equal sides always subtend equal opposite angles.
Can the vertex angle be 180 degrees?
No. A 180-degree angle would make the triangle flat, not a real triangle.
Why must the base angle be less than 90 degrees?
If a base angle were 90 degrees or more, the remaining vertex angle would be zero or negative.
What is the angle sum output for?
It confirms that the computed angles satisfy the triangle rule V+2B=180°.
Can I use decimals for angles?
Yes. Decimal angles are accepted and results are rounded to 6 decimal places.