Triangle angle calculator
Two angles of 50° and 60° leave 70° for the third. Enter the two interior angles you know, in degrees, and get the missing one as 180° minus their sum. Pairs that cannot close a triangle are flagged. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle a
- 50
- Angle b
- 60
- Missing angle
- 70
- Sum known
- 110
- Sum degrees
- 180
- Unit angles
- deg
Every plane triangle has three interior angles that add to exactly one hundred eighty degrees. When two of those angles are already known, the third is not a guess and not a trigonometric solve: it is one hundred eighty minus the first minus the second. Students, tutors, CAD scripts, and exam graders all need that missing interior angle without mixing it up with side-length solvers, special 30-60-90 ratios, or classifiers that already assume all three degrees. This triangle angle calculator accepts two finite interior angles in degrees, rejects any pair that cannot close a Euclidean triangle, and returns the missing angle together with the known sum.
How two interior angles determine the third
In Euclidean plane geometry the interior angles of any triangle add to one hundred eighty degrees. That single identity is the entire algorithm behind this calculator: if you already know two interior angles A and B, the missing interior angle is C equals one hundred eighty minus A minus B. The identity is not a convenience formula that only works for right triangles or for equilateral triangles; it is a theorem about every plane triangle, whether the figure is acute, right, or obtuse.
It fails only when the figure is not a plane triangle at all, which is exactly when the two given angles cannot leave a positive remainder under one hundred eighty degrees. Each given angle must itself be a genuine interior angle: strictly greater than zero and strictly less than one hundred eighty, because a zero angle collapses a vertex and an angle of one hundred eighty degrees or more cannot sit inside a simple triangle.
After those range checks, the calculator still has to refuse pairs such as one hundred plus eighty, or one hundred twenty plus seventy, because those pairs leave a remainder of zero or a negative remainder. A remainder of zero is a degenerate flat figure, not a triangle with positive area. A negative remainder is geometrically impossible.
No sides, no inverse trigonometric functions, and no ambiguous SSA case appear here: two interior angles determine the third uniquely, and that is the only quantity this capability computes.
Where a missing-angle calculator earns its keep
Classrooms and tutoring platforms use a triangle angle calculator so learners can confirm the angle-sum theorem on arbitrary pairs without mixing that one subtraction up with the law of sines, the law of cosines, or a classifier that already wants all three degrees. Drafting macros, simple CAD checks, and geometry notebooks often know two corner readings from a sketch or a survey and only need the third before they can place a dimension, a hatch, or a warning that the figure will not close. Failed validation does not consume balance.
If you later need sides or a type label, call a dedicated sibling rather than stretching this contract.
What you can do with it
Classroom and homework checks
Let students submit two known interior angles and verify the missing third against the angle-sum theorem, including the cases that must be refused.
Exam and LMS auto-grading
Mark missing-angle items with a deterministic oracle that rejects pairs summing to 180 degrees or more instead of returning a dummy zero.
Drafting and sketch close-out
Turn two measured corners from a plan or survey into the third interior angle before placing a dimension or testing whether the figure closes.
FAQ
What happens if the two given angles sum to 180 degrees or more?
A plane triangle cannot have two interior angles that already fill the whole 180 degrees, so those pairs are not billed as a success.
Do the given angles have to be acute?
No. Either angle may be obtuse as long as it is strictly less than 180 degrees and the pair still sums to less than 180. A right angle is also allowed.
Does this calculator need side lengths?
No. Two interior angles determine the third uniquely. Sides, ASA, SAS, and the law of sines are different problems served by other capabilities.
How do I find the third angle of a triangle?
Subtract the two known angles from 180°. With 50° and 60°, the known angles add up to 110°, so the third angle is 70°. No side lengths or trigonometry are needed.
Does this work for right and obtuse triangles?
Yes. The angles of every flat triangle add up to 180°, whether it is acute, right or obtuse. A right angle of 90° with an angle of 30°, for example, leaves 60° for the third corner.
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-angle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle_a":50,"angle_b":60}'const res = await fetch("https://api.kit.forhosting.com/math/triangle-angle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle_a": 50,
"angle_b": 60
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/triangle-angle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle_a": 50,
"angle_b": 60
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/triangle-angle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle_a":50,"angle_b":60}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle_a":50,"angle_b":60}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/triangle-angle", 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": 50,
"angle_b": 60
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.triangle_angle",
"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
How two interior angles determine the third
The endpoint therefore treats any pair whose sum is one hundred eighty degrees or more as invalid_input rather than returning zero or a negative dummy angle. That matches classroom language, which says those two angles cannot belong to the same triangle, and it matches API clients, which treat empty success and hard failure differently for billing and retries.
Input contract, response shape, and error behaviour
Every given angle must be strictly greater than zero and strictly less than one hundred eighty. Example: fifty and sixty degrees yield a missing angle of seventy, because one hundred ten from one hundred eighty leaves seventy. Ninety and thirty yield sixty, a complementary acute angle next to a right angle. One hundred and eighty are refused because they already add to the whole plane and leave no room for a third vertex. Failed validation is not billed. POST a JSON body with two required finite numbers: angle_a and angle_b, the known interior angles in degrees. Aliases A, angle1, and alpha are accepted for the first field; B, angle2, and beta are accepted for the second, so scripts that already use textbook labels do not need a rename step. Each field may arrive as a JSON number or as a numeric string; missing fields, empty strings, and non-finite values fail with invalid_input naming the field. If the known sum is one hundred eighty degrees or more, the request is rejected with a message that a plane triangle cannot have two interior angles that sum to one hundred eighty degrees or more. On success the body echoes angle_a and angle_b, returns missing_angle as one hundred eighty minus that sum, reports sum_known and the constant sum_degrees of one hundred eighty, and includes unit_angles set to deg plus a short formula string. The endpoint does not return side lengths, does not classify the triangle as acute, right, or obtuse, and does not accept a third angle to check; those are different search intents served by other capabilities.
Where a missing-angle calculator earns its keep
Exam-prep generators and LMS auto-graders need a deterministic oracle that marks illegal pairs as invalid_input instead of silently returning zero, which a buggy grader might treat as a successful missing angle. Keep requests small, pin the missing_angle field in tests, and you get a reproducible two-angle check for homework, LMS plugins, and edge workers without standing up a computer-algebra system of your own.
Technical questions
How do I find the missing angle of a triangle from two known angles?
Send two finite interior angles in degrees as angle_a and angle_b. The API returns missing_angle = 180 − angle_a − angle_b when that remainder is a positive interior angle.
What does the triangle angle calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.