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Maths Exercices

Angles: Types and labeling

An angle is a figure formed by two rays with a common endpoint. The shared endpoint is the vertex of the angle.

The symbol < means angle.

An angle can be named in different ways:

  • by a number or letter written inside the angle.
  • by the name of the vertex.
  • by the vertex and a point on each ray.

The four ways to name this angle are: <1, <M, <NMO or <OMN

An angle is measure in degrees. The symbol for degrees is º.

Types of angles:

  • A right angle is an angle whose measure is 90º. A right angle is often identified by a small square drawn inside it.
  • An acute angle is an angle whose measure is larger than 0º but less than 90º.
  • An obtuse angle is an angle whose measure is larger than 90º but less than 180º.
  • A straight angle is an angle whose measure is 180º. Such an angle is, in fact, a straight line.

Special angle pairs.
Certain pairs of angles have special names. Those names are in some cases based upon their positions relative to one another. In other cases they are based upon the angles' degree measures adding up to a certain amount.

Adjacent angles.
Two angles that share a vertex and share a common side that separates them.

Angles 1 and 2 are examples of adjacent angles.

Vertical angles.
When two lines intersect so as to form four angles, the angles on opposite sides of the common vertex are known as vertical angles.

Of the four angles formed at M, <1 and <3 are vertical angles. So are <2 and <4.

Congruent angles.
Congruent angles are angles that have exactly the same measure.

Complementary angles.
Any two angles that add up to 90º are called complementary angles.

<1 and <2 are adjacent complementary angles.
<3 and <4 are nonadjacent complementary angles.

Supplementary angles.
When two angles add up to a total of 180º, they are called supplementary angles.

<5 and <6 are adjacent supplementary angles while <E and <F are nonadjacent supplementary angles.