Angles

 

An angle measures the amount of turn. There are 2 types of angles, Positive and Negative Angles. When measuring from a line,

1) Positive angle goes counterclockwise (or anticlockwise).

2) Negative angle goes clockwise.

Parts of an Angle

1) The corner point of an angle is called the Vertex.

2) And the two straight sides are called Arms.

3)The Angle is the amount of turn between each arm.

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. 

complementary angles

An Acute Angle

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

complementary angles

An Obtuse Angle

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

complementary angles

Complementary Angles

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

complementary angles

Supplementary Angles

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

complementary angles
 

Demonstration:

Given angles a, b, c, d, e and f with measures 

a = 21o

b = 90.1o

c = 90o

d = 134.2o

e = 69o

f = 45.8o

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?

Solution:

Acute Angles are less than 90 degree so a = 21o ,e = 69o, f = 45.8

Obtuse Angles are more than 90 degree and less than 180 thus b = 90.1o, d = 134.2o

Complimentary Angles have their sum measuring 90 degree thus its e = 69o , a = 21o   

Supplementary Angles have their sum measuring 180 degree thus its d = 134.2o, f = 45.8o
1 - a, e and f 
2 - b and d. 
3 - a - e 
4 - d - f