Special Angle Pairs

There are three Special Angle Pairs in Geometry. These angles are the Supplementary Angles, Complementary Angles and the Vertical Angles. Below are the definition and example of each.
Source: http://www.regentsprep.org
Supplementary Angles are two different angles that equal to 180 degrees. They can be only two different angles in a supplementary angle. These angles can be obtuse, acute, or a right angle. It cannot be more than one obtuse angle or an acute angle, because the number will be either too high, or it will be too low. Right angles are different, and two right angles are supplementary angles that equal to 180. An example of a Supplementary Angle on the left from www.regentsprep.org, whichshows that  angle 1 and angle 2 create 180 degree angle which is a supplementary angle.
  



Source: http://www.regentsprep.org

 Complementary Angles are two different angles that equal to 90. They can be only two different angles in a complementary angle. The angles can only be acute angle because anything above an acute angle is higher than 90. The Complementary angle on the left from www.regentsprep.org, shows that angle 1 and angle 2 creates a 90 degree angle.


  
Source: http://www.regentsprep.org
Vertical Angles are two different angles that are opposite rays that form a line. Angles that are opposites from each other equal the same. These angles can be two acute angles or two obtuse angles that equal the same to each other. The Vertical Angles on the left from  www.regentsprep.org shows that Angle 1 and 3 is Vertical as well as Angles 2 and 4. 





How do each one of them:
Supplementary Angles*:

  1. Identify the supplementary angles and draw a diagram
  2. Write the standard equation. (Angle 1 + Angle 2 = 180)
  3. Substitute the values of ∠ 1 and ∠ 2
  4. Solve for x.
Complementary Angles*:
  1. Identify the supplementary angles and draw a diagram
  2. Write the standard equation. (Angle 1 + Angle 2 = 90)
  3. Substitute the values of ∠ 1 and ∠ 2
  4. Solve for x.
Vertical Angles*:
  1. Identify the supplementary angles and draw a diagram
  2. Write the standard equation. (Angle 1 = Angle 2)
  3. Substitute the values of ∠ 1 and ∠ 2
  4. Solve for x.
*Notes from my teacher, Ms. Koltunova & Mr. Perry
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