ANGLES: DEFINITIONS AND BASIC CONSTRUCTIONS

3. Angles

3.1 DEFINITION

In geometry, an angle is the figure formed by two rays, called the arms of the angle, sharing a common endpoint, called the vertex of the angle. An angle measures the amount of turn. It is measured in degrees. 

We label the angles using a Greek letter like α (alpha) or θ (theta)

3.2. TYPES OF ANGLES

• ACUTE ANGLES (Ángulos agudos): angles smaller than right angles (less than 90°)
  
• RIGHT ANGLES (ángulos rectos): angles equal to 90º. 
  
• STRAIGHT ANGLES (ángulos llanos): angles equal to 180º. 
  
• OBTUSE ANGLES (ángulos obtusos): angles larger than a right angle and smaller than a straight angle (between 90° and 180°) 
  
• REFLEX ANGLE (ángulo cóncavo): angles between 180º and 360º
  
• ROUND OR FULL ANGLES (ángulos completos) : angles equal to 360º.
  

 3.2. COMPLEMENTARY AND SUPPLEMENTARY ANGLES

Two angles are Complementary when they add up to 90 degrees (a Right Angle ).

 Two Angles are Supplementary when they add up to 180 degrees.

How to remember which is which? Easy! Think:

• "C" of Complementary stands for "Corner" (a Right Angle), and
• "S" of Supplementary stands for "Straight" (180 degrees is a straight line)

3.3.COPYING AN ANGLE

If we want to draw an angle equal to a given one with vertex at a given point V, we must follow the next steps:

3.3.ANGLE BISECTOR

The angle bisector is a line which divides the angle in two equal parts. Each point of an angle bisector is equidistant from the sides of the angle. 

 

3.4. DRAWING ANGLES WITH THE SET SQUARE RULERS

3.5.  ADDING AND SUBTRACTING ANGLES WITH THE COMPASS

The addition of two angles is another angle whose measure is the addition of the measures of those two angles.

The subtraction of two angles is another angle whose measure is the subtraction of the measures of those two angles.