The Mathematical Symbol "Measured Angle (∡)"

The ∡ Symbol in Mathematics: Measured Angle

Mathematics is adorned with symbols that succinctly represent intricate concepts. Among them is the ∡ symbol, which stands for the "Measured Angle". This article offers a glimpse into the significance and usage of the ∡ symbol, complemented by relevant examples.

Usage

The ∡ symbol is predominantly utilized in geometry to represent angles that have been measured or specified. Unlike the general angle symbol (∠), the ∡ conveys that a particular angular measurement is being discussed or has been determined.

Examples

  • Example 1: When detailing the angles of a triangle, one might encounter notations like:
    \( \angle ABC = 45^\circ \)
    However, to emphasize the measured nature of the angle, one can use:
    \( ∡ ABC = 45^\circ \)
  • Example 2: In trigonometry, when referencing specific known angles, the ∡ notation can be employed for clarity. For instance:
    If \( ∡ A = 30^\circ \), then \( \sin(∡ A) = 0.5 \).
    Here, the ∡ emphasizes that we are working with a specific measured angle, not just any angle labeled A.

In summary, the ∡ symbol provides an enhanced layer of specificity in geometrical and trigonometric contexts. By designating measured or specified angles, it fosters clarity and precision in mathematical communication.

Mathematical symbol 'Measured Angle'

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Codes for the ∡ Symbol

The Symbol∡
Alt CodeAlt 8737
HTML Code∡
HTML Entity∡
CSS Code\2221
Hex Code∡
UnicodeU+2221

How To Insert the ∡ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∡ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8737. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8737;</b>My symbol: ∡

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &angmsd;</b>My symbol: ∡

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
<style>
span:after {
content: "\2221";}
</style>
<span>My symbol:</span> 		My symbol: ∡

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x2221;</b>My symbol: ∡
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2221 to place the ∡ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

∡

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∡ is U+2221. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
2221
[Hold down Alt]
[Press x]		∡
(The 2221 turns into ∡. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2221. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2221"
document.write("My symbol: " + str)		My symbol: ∡