Triangle degree calculator
Angles of 60° and 40° leave 80° for the third corner. Type the two interior angles you measured, in degrees, and the third comes from subtracting both from 180°, after each value is checked so an impossible pair is refused. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle a
- 60
- Angle b
- 40
- Angle c
- 80 deg
The interior angles of every Euclidean triangle add up to exactly one hundred eighty degrees. That single fact is enough to recover a missing angle once two others are known: subtract both given measures from one hundred eighty and the remainder is the third vertex. This triangle degree calculator accepts two interior angles in degrees, checks that each is a positive finite number strictly less than one hundred eighty, and returns the complementary third angle.
Why two angles fix the third vertex
In Euclidean plane geometry the interior angles of a triangle always add to one hundred eighty degrees. That angle-sum theorem is not a slogan: it follows from drawing a line through one vertex parallel to the opposite side and reading the alternate interior angles, and it is the reason a third vertex is completely determined once two angles are known. If angle A is sixty degrees and angle B is forty degrees, then angle C is one hundred eighty minus sixty minus forty, which is eighty degrees.
The same subtraction works for a right triangle—ninety plus thirty-five leaves fifty-five—and for an obtuse triangle—one hundred twenty plus twenty-five leaves thirty-five. Degenerate cases matter as much as the happy path. If A and B already add to one hundred eighty, the third angle would be zero and the three points would lie on a straight line rather than enclose a triangular region.
If they add to more than one hundred eighty, the remainder is negative, which no interior angle can be. Each given angle must itself be strictly between zero and one hundred eighty: a zero-degree corner is not a vertex of a proper triangle, and an angle of one hundred eighty degrees or more cannot sit inside one either. Sides are not required.
The law of sines and the law of cosines recover angles from sides; here the search intent is the complementary degree after two angles are already measured, so the algorithm is a single subtraction with explicit geometric guards.
Where a triangle degree calculator earns its keep
Classrooms and tutoring platforms use a triangle degree calculator so learners can check the angle-sum step without arithmetic slips when two vertices are already marked on a figure. Exam-prep generators need a deterministic oracle that marks wrong the case of a pair that already sums to one hundred eighty or more, instead of silently returning zero that a buggy grader might treat as success. Game and CAD pipelines that store polygons by two known interior angles can recover the third corner in one request before triangulation.
Failed validation does not consume balance. Keep requests small, pin the rounded third angle in tests, and you get reproducible degrees for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own.
What you can do with it
Classroom and homework checks
Let students enter two interior angles in degrees and verify the third against the Euclidean angle-sum theorem used in textbooks.
Exam and LMS auto-grading
Mark missing-angle items with a deterministic oracle that rejects a pair summing to 180 degrees or more and never invents a third vertex.
Truss, panel, and CAD corners
Recover the remaining interior angle of a triangular panel or roof truss after two corners have been measured on site or in a drawing.
FAQ
What happens if the two angles sum to 180 degrees or more?
A pair that already sums to 180 degrees or more cannot form a triangle, because the third interior angle would be zero or negative.
Do the angles have to be in degrees?
Yes. This triangle degree calculator works in degrees only. Convert radians to degrees first if your instrument or script reports in radians.
Can I use this for a right triangle?
Yes. Send 90 as one of the given angles and the other known acute angle; the response is the remaining acute angle. A pair such as 90 and 90 is rejected because those two already sum to 180.
Why do the angles of a triangle add up to 180 degrees?
Draw a line through one corner parallel to the opposite side. The two angles it forms with the other sides match the triangle's other two angles, and together with the third they fill a straight line, which is 180°.
Can one of the given angles be 0° or 180°?
No. Each angle must be strictly between 0° and 180°. A corner of 0° is not a real vertex, and an angle of 180° or more cannot fit inside a triangle, so the calculator asks for another value.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/triangle-degree \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle_a":60,"angle_b":40}'const res = await fetch("https://api.kit.forhosting.com/math/triangle-degree", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle_a": 60,
"angle_b": 40
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/triangle-degree",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle_a": 60,
"angle_b": 40
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/triangle-degree", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle_a":60,"angle_b":40}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle_a":60,"angle_b":40}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/triangle-degree", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"angle_a": 60,
"angle_b": 40
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.triangle_degree",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
If the two given angles already sum to one hundred eighty degrees or more, they cannot sit in a triangle—the third angle would be zero or negative—and the task fails with invalid_input instead of inventing a hollow result.
Why two angles fix the third vertex
This calculator therefore treats a sum of one hundred eighty degrees or more as invalid_input rather than returning a zero or negative third angle that a sloppy grader might treat as success.
Input contract, response shape, and error behaviour
Units are degrees only; convert radians to degrees before calling if your instrument reports in radians. POST a JSON body with two required finite numbers: angle_a and angle_b, the known interior angles in degrees. Each field may arrive as a JSON number or as a numeric string; aliases a and angle1 for the first angle, and b and angle2 for the second, are accepted so scripts can reuse common textbook names. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes angle_a and angle_b, returns angle_c rounded to twelve decimal places for stable goldens across runtimes, sets unit to deg, and includes the formula string C equals one hundred eighty minus A minus B. Example: angle_a equals sixty and angle_b equals forty yields angle_c eighty, because one hundred eighty minus one hundred is eighty. Pair the response with your own drawing code if you need a sketch of the three vertices; this endpoint solves for the missing degree only and does not emit side lengths, plots, or step-by-step prose beyond the formula field.
Where a triangle degree calculator earns its keep
Survey, carpentry, and craft notebooks often measure two corners of a triangular panel or roof truss and need the remaining corner before cutting; calling a tiny parse API avoids pulling a full computer-algebra system for one subtraction.
Technical questions
How do I find the third angle of a triangle from two given angles?
Send finite numbers angle_a and angle_b in degrees, each strictly between 0 and 180. The API returns angle_c = 180 − angle_a − angle_b, the missing interior angle.
What does the triangle degree calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.