what are some angles that can be named with one vertex?

Question

I need examples

Answer 1

This would be a lot easier to explain with a diagram, but there are no drawing tools in this app, so.......

Imagine the letter "V". It's basically an angle. Just one. The vertex is the point of the "V".

Now imagine the letter "X". It consists of four adjacent angles (not to mention the larger angles created by adding the adjacent angles together) with a common vertex. The common vertex is where the two lines forming the "X" intersect.

Imagine a math diagram that looks like a "V", and the vertex has a letter name, say "A". If I talk about "angle A" it's clear which angle I'm talking about. There's only one angle in the diagram.

Imagine now a math diagram that looks like an "X", and the intersection point of the two segments that make the "X", the common vertex of the angles, has a letter name, say "B". If I talk about "angle B", it's unclear which of the four angles (or the larger angles consisting of two or more adjacent angles) I'm talking about, since multiple angles have the same vertex. I would need more information to name a particular angle, namely two endpoints of two of the segments making the "X".

To sum up, you can name an angle with one letter when there is only one angle that has the vertex named by the letter.

When more than one angle shares a vertex, you have to use three letters, one on each ray or segment of the angle you're interested in, with the vertex in the middle.

Answer 2

Use these terms and do an Internet seach for the examples.

TERM                 ANGLE DEFINITION

Included             The angle made by two lines with a common vertex.
                         This term is the one that includes all the following
                         angles terms. It is the superset.

Angles from a protractor (for a circle):
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acute                  greater than 0 degrees and less than 90 degrees
right                   90 degrees
obtuse                greater than 90 degrees and less than 180 degrees
straight               180 degrees (vertex attaches 2 half lines going opposite directions)
reflex                  greater than 180 and less than 360 degrees
full rotation          360 degrees (vertex attaches 2 half lines that are the same)

Angles from two intersecting lines:
-----------------------------------
adjacent              formed when two intersecting lines form angles
                          that are supplimentary (side by side) to each other.
                          The sum of the degrees when both angles are added = 180.
                          They share a vertex, share the same two lines,
                           and share one common arm (portion) on those lines.
                           vertical formed when two intersecting lines form angles that
                           share a common vertex, share the same two lines,
                           but share no common arms (portions) of those lines.

opposite               same definition as vertical. They share the same vertex.

When angles are created by a transversal line intersecting with two
parallel lines, we also get these angles:
-------------------------------------------------------------------
corresponding       angles with the same degree on both parallel lines,
                           on the SAME side of the transveral line
alternating            angles with the same degree on both parallel lines,
                           on the OPPOSITE side of the transversal line.

Angles in an isosceles triangle:
--------------------------------
vertex                  angle formed by the two congruent (equal) sides
base                    angle formed by the base (non equal) side
                           note: the other side is one of the congruent sides.

Angles inside and outside a polygon:
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interior                 angles created inside the polygon shape,
                           formed by two sides and the vertex attaching them
exterior                angles formed by an adjacent angle (see above) for
                           the sides that reside on a line.