# 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).

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### Angle of a triangle in a cube

Find the angle of a triangle in a cube. I don't how to start on this problem. The only I have noticed is that it may be a isosceles triangle so the two angle should be the same. Can somebody give me ...
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### Calculate the distance of any point on the arc from the center of circle

This is my first time posting so I hope my formatting is correct. Consider this, I have two circles, one big one small with radius $r_1$ and $r_2$. The borders of both circles are touching. See image: ...
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### Best way to describe the angle from another ray on a circle [closed]

What I have is $3$ rays each of whose origin is the same. Ray $Z$ is always $0^{\circ}$ and ray $X$ and ray $Y$ is a random angle away from ray $Z$ in a clockwise direction. What is the best way to ...
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### How can I show that the angle between any two categorical points is between [0°,90°]? [closed]

I'm currently studying Bivariate Analysis of categorical values, but I don't know how to answer this question.
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### How to get the opposite angle?

I have been looking for the answer to this question but I haven’t found anything related. I will use the following image as an example. As you can see, there is a circle divided in different parts of ...
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### Substituting the Angle Between Two Complex Vectors to Vector Product Addition

As in this paper, the angle between two complex vectors $u,v\in\mathbb{C}$ may be taken as: $$\cos(\theta)=\frac{\text{Re}(u\cdot v)}{|u\cdot v|},$$ where $\text{Re}$ takes the real part of the dot ...
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### How many angles can be drawn using only a ruler and a compass?

So far I know that it’s possible to draw angles which are multiples of 15° (ex. 15°, 30°, 45° etc.). Could anybody please tell me if it's possible to draw other angles which are not multiples of 15° ...
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### In triangle $\triangle ABC$, angle $\angle B$ is equal to $60^\circ$; bisectors $AD$ and $CE$ intersect at point $O$. Prove that $OD=OE$.

In triangle $\triangle ABC$, angle $\angle B$ is equal to $60^{\circ}$; bisectors $AD$ and $CE$ intersect at point $O$. Prove that $OD=OE$. So I've already made a diagram(it is attached below), but I ...
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### The bisector of the exterior angle at vertex C of triangle ABC intersects the circumscribed circle at point D. Prove that AD=BD

The bisector of the exterior angle at vertex $C$ of triangle $ABC$ intersects the circumscribed circle at point $D$. Prove that $AD=BD$. So what I'm wondering is how to prove this? I've already drawn ...
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### Mixtilinears and Symmedians

(this is from EGMO) Prove that angles ATK and LTI are equal. The hint in the book was about symmedians. I am not sure how to prove that line segment AT is the T symmedian, angle chasing did not work, ...
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### Find the angle θ (all the circles are tangent)

In the following figure ABCD is a side square $\alpha$, the points $P_0, P_1, P_2, P_3, Q_0, Q_1, Q_2, Q_3, X \ and \ Y$ are points of tangency, $BC \ and \ ZB$ are the diameters, respectively, of the ...
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### Proving an approximate angle trisection by compass and straightedge

My 70 year old father has given the below explanation. Can some one please verify or point out deficiencies if any. The geometrical problem of trisecting any given angle by using compass and a ...
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### Angle Proof Inside Circle

The vertex of angle $\angle BAC$ lies inside of a circle. Prove that the value of angle $\angle BAC$ is equal to half the sum of angle measures of the arcs of the circle confined inside angle itself ...
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### Calculate the angle of $\theta$ in pythagoreans theorem with different units for the Adjacent and Opposite sides

In the above image I know the value of the adjacent side. It's $298$. I know the value of the opposite side it's $806.8$. The problem is $298$ is in units of 'bars' on a stock chart and the value ...
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### How to measure the angle between two parallel lines?

In some geometries, parallel lines "meet/touch/coincide" at infinity. This being the case, there must necessarily be an angle between them. I was wondering what the "value" of this ...
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### Find an angle created by lateral edge and the base of the Pyramid

Pyramid $SABC$ has right triangular base $ABC$, with $\angle{ABC}=90^\circ$. Sides $AB = \sqrt3, BC = 3$. Lateral lengths are equal and are equal to $2$. Find the angle created by lateral length and ...
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### If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines… find the value of $|A|$.

If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines with angle of intersection $'\theta'$ then find the value of |A|. I tried using general equation of ...