Angles in Geometry

Definitions and properties of angles in geometry.

An Angle in Geometry

An angle is the rotation required to superimpose one of two intersecting lines on the other.

A Right Angle

A right angle is an angle with measure equal to 90 degrees.

An Acute Angle

An acute angle is an angle with a measure between 0 and 90 degrees.

An Obtuse Angle

An obtuse angle is an angle with a measure between 90 and 180 degrees.

Complementary Angles

Two angles are complementary if the sum of their measures is equal to 90 degrees.

Example: angles a and b with measures a = 19
o and b = 71o are complementary since a + b = 90o

Supplementary Angles

Two angles are supplementary if the sum of their measures is equal to 180 degrees.

Example: angles a and b with measures a = 122.1
o and b = 57.9o are supplementary since a + b = 180o

Exercises

(see solutions below) Given angles a, b, c, d, e and f with measures

a = 21
o

b = 90.1
o

c = 90
o

d = 134.2
o

e = 69
o

f = 45.8
o

1 - Which of these angles are acute?

2 - Which of these angles are obtuse?

3 - Which pairs of angles are complementary?

4 - Which pairs of angles are supplementary?

Solutions to Above Exercises

1 - a, e and f

2 - b and d.

3 - a - e

4 - d - f

More geometry references
Geometry Tutorials, Problems and Interactive Applets.