# Questions tagged [angle]

An object formed by two rays joining at a common point, or a measure of rotation. In the latter form, it is commonly in degrees or radians. Please do not use this tag just because an angle is involved in the question/attempt; use it for questions where the main concern is about angles. This tag can also be used alongside (geometry).

827 questions
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### Finding an Angle using Cyclic Quadrilateral and Circle Theorems

To find angle BGE from the diagram above, a proof was proposed: "Angle BCF equals 100 degrees (external to triangle ACB); ADEC and DBFC are cyclic quadrilaterals -> angle ADE equals 100 degrees; ...
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### Proof Regarding Tangents

There are two circles: $C1$ and $C2$. They touch internally at point B (note that C1 is inside of C2). C1 has a chord BC, which is produced to meet C2 at D. The tangent from C meets the common tangent ...
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### $\cos(a)=4/5$, $\sin(b)=12/13$, what is $\sin(c)$?

$\cos(a)=4/5$, $\sin(b)=12/13$, what is $\sin(c)$? with $a,b,c < \frac{\pi}{2}$. Attempt : Since $\sin^{2}(a) = 1 - \cos^{2}(a)$, I get $\sin(a) = \frac{3}{5}$. But how to get $\sin(c)$? I have ...
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### $\tan(a) = 3/4$ and $\tan (b) = 5/12$, what is $\cos(a+b)$

It is known that $$\tan(a) = \frac{3}{4}, \:\:\: \tan(b) = \frac{5}{12}$$ with $a,b < \frac{\pi}{2}$. What is $\cos(a+b)$? Attempt : $$\cos(a+b) = \cos(a) \cos(b) - \sin(a) \sin(b)$$ And we ...
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### How is an angle's degree determined?

To be as specific as possible I am not asking the following: What is a degree? (Measurement of rotation between two intersecting rays/lines) How much is a degree? ($\frac{1}{360}$th rotation of a ...
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### Finding Angle BDF inside a circle

Find Angle BDF What i tried Since Angle AOE is twice Angle ACE, we have Angle ACE= $(360-214)/2=73$ degrees. Angle OET and Angle TAO is $90$ degrees since its a tangent line to the circle. Angle ...
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### Why only two dihedral angles for a snub dodecahedron?

The Wikipedia page for the snub dodecahedron provides explicit coordinates for its vertices, from which one can of course by brute force calculate that there are only two dihedral angles. Can anyone ...
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### How to create a point behind another point given an angle?

I have a point A and a radian angle value R (image below describes this heading system) that represents a heading from point A. How do I create a point B that is a small, fixed distance (like 1.0 ...
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### Is a single line, line segment, or ray a valid angle?

After online research and several definitions of the term angle it seems they all fit a short set of restrictions for what defines an angle, "a shape formed by two rays that intersect at a point ...
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### Can a Point on a Clockwise Circuit that isn't clockwise Increase the Visibility to Other Potential Circuit Points?

Given a fully connected graph of 2-dimensional points: I and a 2-dimensional point G I want to select points from I to create a clockwise circuit around G. Given that I have already selected 2 points:...
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### Name and number of “equilateral tessellations with same angles on all vertexes”

Longer background, shorter questions below: Tessellations of 2D plane consisting of regular polygons are usually described with vertex configurations such as "3.4.6.4" meaning that there are a ...