The arm of an angle is the line segment that connects the vertex of the angle to one of its endpoint. It is one of the two rays that form the angle.
The vertex of an angle is the point at which the two rays meet to form the angle. The rays are the two sides of the angle that extend indefinitely in opposite directions.
There are three types of angles based on the measure of the angle: acute, right, and obtuse. An acute angle is an angle that measures less than 90 degrees. A right angle is an angle that measures exactly 90 degrees. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.
Here are five examples of angles with their arms labeled:
Example 1:
[asy]
pair A,B,C;
A=(0,0);
B=(4,0);
C=(0,3);
draw(A–B–C–cycle);
draw(A–C);
label(“A”,A,SW);
label(“B”,B,SE);
label(“C”,C,N);
label(“$\angle ABC$”,B,S);
[/asy]
In this example, the angle is $\angle ABC$, and the vertex is point B. The arms of the angle are line segments $\overline{AB}$ and $\overline{BC}$.
Example 2:
[asy]
pair A,B,C;
A=(0,0);
B=(4,0);
C=(4,3);
draw(A–B–C–cycle);
draw(A–C);
label(“A”,A,SW);
label(“B”,B,SE);
label(“C”,C,N);
label(“$\angle ACB$”,C,NW);
[/asy]
In this example, the angle is $\angle ACB$, and the vertex is point A. The arms of the angle are line segments $\overline{AC}$ and $\overline{AB}$.
Example 3:
[asy]
pair A,B,C;
A=(0,0);
B=(4,0);
C=(0,3);
draw(A–B–C–cycle);
draw(B–C);
label(“A”,A,SW);
label(“B”,B,SE);
label(“C”,C,N);
label(“$\angle BAC$”,A,NE);
[/asy]
In this example, the angle is $\angle BAC$, and the vertex is point A. The arms of the angle are line segments $\overline{BA}$ and $\overline{AC}$.
Example 4:
[asy]
pair A,B,C;
A=(0,0);
B=(4,0);
C=(4,3);
draw(A–B–C–cycle);
draw(B–C);
label(“A”,A,SW);
label(“B”,B,SE);
label(“C”,C,N);
label(“$\angle BCA$”,C,NE);
[/asy]
In this example, the angle is $\angle BCA$, and the vertex is point C. The arms of the angle are line segments $\overline{BC}$ and $\overline{CA}$.
