Triangle Calculator · Practical guide
How to Find the Third Angle of a Triangle
Every triangle's angles total exactly 180°, so two known angles always reveal the third by simple subtraction.
At a glance
The Answer
Subtract the two known angles from 180°: C = 180° − A − B. If a triangle has angles of 90° and 35°, the third is 180 − 90 − 35 = 55°. No exceptions — in standard geometry the interior angles of every triangle sum to exactly 180°.
Interactive tool
Triangle Calculator
Enter your own values, then compare the result with the examples below.
Triangle Solution
Why It Always Works
Draw a line through any vertex parallel to the opposite side and the alternate interior angles show the three corners lying flat along a straight line — 180° by definition. That's why this rule holds for every triangle: acute, right, obtuse, scalene, or equilateral.
Quick Reference
| Angle A | Angle B | Third Angle | Triangle Type |
|---|---|---|---|
| 60° | 60° | 60° | Equilateral (acute) |
| 30° | 60° | 90° | Right |
| 45° | 55° | 80° | Acute |
| 100° | 40° | 40° | Obtuse isosceles |
| 90° | 45° | 45° | Right isosceles |
From Angles to a Full Solution
The third angle alone doesn't fix the triangle's size, but add any one side and everything else follows. Enter the two angles and a side in the ASA or AAS tab above to get all three sides, the area, the perimeter, and the triangle type in one step.
Frequently Asked Questions
Do a triangle's angles always add up to 180 degrees?
Yes, in standard Euclidean geometry the three interior angles total exactly 180°. Only in curved (non-Euclidean) geometry, like on a sphere, can the sum be larger.
What if my two angles already total 180° or more?
Then no triangle exists — nothing is left for the third angle. The calculator rejects angle pairs that sum to 180° or above.
Can a triangle have two right angles?
No. Two 90° angles would already total 180°, forcing the third angle to be 0°, which collapses the triangle into a line segment.
How do I classify a triangle from its angles?
Look at the largest angle: under 90° means acute, exactly 90° means right, and over 90° means obtuse.