Q: What is the number of straight angles that can be drawn through two points?

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Yes, 2 angles can have 3 points in common. Two angles of the same number of degrees can be superimposed on each other and would share all points. Or, you could choose 3 points on one line segment, while having two other line segments which do not share points, and which delineate different angles.

A straight line, through the origin, with a gradient of 1/2.

Origin

line segments

Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.

Related questions

In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.

1 straight line. An infinite number of curved lines.

You need two points to determine a line. A single point can have an infinite number of lines passing through it.

An ellipse is a conic section, a curving line which is the path of a point that moves in such a way that the sum of its distance from two fixed points is constant.... so no - there are not 4 straight angles in an ellipse, nor any straight bits at all.

Yes, 2 angles can have 3 points in common. Two angles of the same number of degrees can be superimposed on each other and would share all points. Or, you could choose 3 points on one line segment, while having two other line segments which do not share points, and which delineate different angles.

== == Through any two points there is exactly one straight line.

It is the shortest distance between two points.

A straight line, through the origin, with a gradient of 1/2.

Origin

It is an collection of an infinite number of points.

Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.

line segments