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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.

angle definition

A Right Angle

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

right angle

An Acute Angle

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

acute angle

An Obtuse Angle

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

obtuse angle

Complementary Angles

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

complementary angles


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.

complementary angles


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.