Angle Theorems

Summary

Angle theorems help in understanding and calculating unknown angles using relationships between different types of angles. There are six types of angles based on their degree measurement: acute, right, obtuse, straight, reflex, and full rotation angles.

• Acute angle — An angle less than 90⁰.
  Example: A slice of pizza encloses an acute angle.
• Right angle — An angle of exactly 90⁰.
  Example: The angle of a set square is a 90⁰ angle.
• Obtuse angle — An angle between 90⁰ and 180⁰.
  Example: The top part of a hanger has an obtuse angle.
• Straight angle — An angle of exactly 180⁰.
  Example: All rulers consist of 180⁰ angles.
• Reflex angle — An angle between 180⁰ and 360⁰.
  Example: Reflex angles can be made by the positions of the clock hands at 9 o'clock.
• Full rotation angle — An angle of 360⁰.
  Example: A CD represents a 360⁰ angle.
• Complementary angles — Two angles that add up to 90⁰.
  Example: Angles A and B are complementary if A + B = 90⁰.
• Supplementary angles — Two angles that add up to 180⁰.
  Example: Angles C and D are supplementary if C + D = 180⁰.
• Vertically opposite angles — Angles that are equal when two lines intersect.
  Example: If two lines intersect, angles a and b are vertically opposite and equal.
• Corresponding angles — Angles that are equal when a transversal cuts two parallel lines.
  Example: Angles in the 'F' shape are corresponding and equal.
• Alternate angles — Angles that are equal when a transversal cuts two parallel lines.
  Example: Angles in the 'Z' shape are alternate and equal.
• Co-interior angles — Angles that add up to 180⁰ when a transversal cuts two parallel lines.
  Example: Angles in the 'C' shape are co-interior and supplementary.

Exam Tips

Key Definitions to Remember

• Acute angles are less than 90⁰.
• Right angles are exactly 90⁰.
• Obtuse angles are between 90⁰ and 180⁰.
• Straight angles are exactly 180⁰.
• Reflex angles are between 180⁰ and 360⁰.
• Full rotation angles are 360⁰.
• Complementary angles add up to 90⁰.
• Supplementary angles add up to 180⁰.
• Vertically opposite angles are equal.
• Corresponding angles are equal.
• Alternate angles are equal.
• Co-interior angles add up to 180⁰.

Common Confusions

• Confusing complementary and supplementary angles.
• Misidentifying alternate and corresponding angles.
• Forgetting that vertically opposite angles are always equal.

Typical Exam Questions

• What is the measure of an angle that is complementary to a 30⁰ angle? 60⁰
• If two angles are supplementary and one is 110⁰, what is the other angle? 70⁰
• Find the value of x if two vertically opposite angles are given as 3x and 75⁰. x = 25⁰

What Examiners Usually Test

• Ability to identify and calculate different types of angles.
• Understanding of angle relationships in parallel lines cut by a transversal.
• Application of angle theorems to solve geometric problems.