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

Right Angle

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

Straight Angle

A straight angle is an angle with measure equal to 180 degrees.
straight 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 degree.
complementary angles

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

Supplementary Angles

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

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

Exercises (see solutions below)

Given angles a, b, c, d, e and f with measures
a = 21°
b = 90.1°
c = 90°
d = 134.2°
e = 69°
f = 45.8°
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 References and Links to Geometry Tutorials

Questions on Angles with Solutions and Explanations
Geometry Tutorials and Problems