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I see in some math formulation that a certain angle is called, let's say

$$\angle ABC$$

but there is a letter put in front of the angle notation.

$$m\angle ABC$$

What does the $m$ represent here? A factor?

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  • $\begingroup$ Try to use LaTeX to write accurately mathematics here. You also didn't write what the angle is called, "let say..." $\endgroup$ – DonAntonio Oct 30 '13 at 17:23
  • $\begingroup$ <ABC and m<ABC.. I dont know why it doesnt show up in the question.. $\endgroup$ – Hilbert Oct 30 '13 at 17:24
  • $\begingroup$ Do you mean $\theta(x)$? $\endgroup$ – Don Larynx Oct 30 '13 at 17:24
  • $\begingroup$ You're going to give more context, for example to write down a complete exercise. The letter $\;m\;$ is many times reserved for slope in analytic geometry. $\endgroup$ – DonAntonio Oct 30 '13 at 17:25
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    $\begingroup$ It's because the < hides the subsequent text when the post is rendered. I have fixed it. $\endgroup$ – Cameron Buie Oct 30 '13 at 17:26
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$\angle ABC$ : The angle ABC

$m\angle ABC$: The measure of $\angle ABC$

So, when $\angle ABC \cong \angle DFG$ , that means, $m\angle ABC = m\angle DFG$

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The notation $m\angle ABC$ typically denotes "the measure of angle $ABC$."

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    $\begingroup$ To clarify, the $m$ is sometimes used to distinguish between the measure of the angle ($m\angle ABC$ = a number, in degrees/radians) and the actual angle itself (the geometric object $\angle ABC$). $\endgroup$ – angryavian Oct 30 '13 at 17:29
  • $\begingroup$ Thanks for all your replies and Cameron has understood the badly formulated question correct. But if the angle is, lets say <ABC = 50 degrees. What is the need of m<ABC then? Doesnt <ABC already denote the measure of the angle? $\endgroup$ – Hilbert Oct 30 '13 at 17:31
  • $\begingroup$ @Hilbert No, $\angle ABC$ is used to denote the angle itself, as a geometric object. Of course, this is a minor distinction, and some authors may choose to be lax in the notation. $\endgroup$ – angryavian Oct 30 '13 at 17:36
  • $\begingroup$ @Hilbert: As blf points out, $\angle ABC$ denotes the angle, itself, while $m\angle ABC$ is its measure. For example, suppose we have an equilateral triangle with vertices $A,B,C.$ Then $\angle ABC$ occurs at the intersection of the segments $AB$ and $BC$, while $m\angle ABC$ is the measure of that angle. The distinction isn't always important, but sometimes it is. $\endgroup$ – Cameron Buie Oct 30 '13 at 17:36
  • $\begingroup$ Thanks Cameron & blf.. Perfectly explained. I have been searching for geometry textbooks that explains things like this and deals with elementary things like Congruence, Arc, Geometric shapes like triangles and so on. Any recommendations? $\endgroup$ – Hilbert Oct 30 '13 at 19:33
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∠ABC refers to the physical angle itself while m∠ABC refers to its measure. There isn't any difference between these two and it is absolutely correct to use any of them...Some people just want to formalize things; these people think-"I have a car that is priced at 50000dollars, so i am driving a car and not 50000dollars" and so want to differentiate between little everything.

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