Study Notes
This topic covers the different types of angles, lines, and triangles, and how to calculate unknown angles using angle relationships.
- Acute Angle — an angle less than 90° Example: An angle measuring 45°
- Right Angle — an angle exactly 90° Example: The angle in a square corner
- Obtuse Angle — an angle greater than 90° but less than 180° Example: An angle measuring 120°
- Straight Angle — an angle exactly 180° Example: A straight line
- Reflex Angle — an angle greater than 180° but less than 360° Example: An angle measuring 270°
- Complete Revolution — an angle of 360° Example: A full circle
- Complementary Angles — two angles that add up to 90° Example: Angles of 30° and 60°
- Supplementary Angles — two angles that add up to 180° Example: Angles of 110° and 70°
- Vertically Opposite Angles — angles that are equal when two lines intersect Example: Angles opposite each other at an intersection
- Corresponding Angles — angles that are equal when a transversal cuts two parallel lines Example: Angles in matching corners
- Alternate Angles — angles that are equal when a transversal cuts two parallel lines Example: Angles on opposite sides of the transversal
- Co-Interior Angles — angles that add up to 180° when a transversal cuts two parallel lines Example: Angles on the same side of the transversal
- Scalene Triangle — a triangle with no equal sides Example: A triangle with sides 3 cm, 4 cm, and 5 cm
- Isosceles Triangle — a triangle with two equal sides and angles Example: A triangle with two sides of 5 cm each
- Equilateral Triangle — a triangle with all sides and angles equal Example: A triangle with all sides 6 cm
- Angle Sum of a Triangle — the sum of interior angles in a triangle is 180° Example: Angles of 60°, 60°, and 60° in an equilateral triangle
- Exterior Angle of a Triangle — equals the sum of the opposite interior angles Example: An exterior angle of 120° with interior angles of 70° and 50°
Exam Tips
Key Definitions to Remember
- Acute angles are less than 90°
- Right angles are exactly 90°
- Obtuse angles are greater than 90° but less than 180°
- Straight angles are exactly 180°
- Reflex angles are greater than 180° but less than 360°
- Complementary angles add up to 90°
- Supplementary angles add up to 180°
- Vertically opposite angles are equal
- Corresponding angles are equal
- Alternate angles are equal
- Co-interior angles are supplementary
Common Confusions
- Confusing complementary and supplementary angles
- Misidentifying corresponding and alternate angles
- Forgetting that the sum of angles in a triangle is always 180°
Typical Exam Questions
- What is the size of an angle if it is complementary to a 30° angle? 60°
- If two angles are supplementary and one is 110°, what is the other angle? 70°
- What is the exterior angle of a triangle if the opposite interior angles are 50° and 60°? 110°
What Examiners Usually Test
- Understanding and identifying different types of angles
- Calculating unknown angles using angle relationships
- Applying properties of triangles to solve problems