Lines and Angles • Topic 2 of 3

Types of Angles

An angle is formed when two rays meet at a common point called the vertex. Angles are measured in degrees (°).

Three main types of angles:

  • Acute Angle: Less than 90 degrees (sharp, like the tip of a pencil)
  • Right Angle: Exactly 90 degrees (like the corner of a square)
  • Obtuse Angle: Between 90 and 180 degrees (wider than a right angle)

A straight angle = 180 degrees (a straight line).

Types of Angles45 degreesAcute < 90Right = 90120 degreesObtuse: 90-180
Solved Examples
1
Worked Example
Classify these angles: 45 degrees, 90 degrees, 135 degrees.
Solution45 degrees: Acute (less than 90). 90 degrees: Right angle (exactly 90). 135 degrees: Obtuse (between 90 and 180).
2
Worked Example
A clock shows 3:00. What type of angle do the hands make?
SolutionAt 3:00, the minute hand points to 12 (top) and the hour hand points to 3 (right). The angle between them is exactly 90 degrees — a Right Angle.
3
Worked Example
If angle A = 35 degrees and angle B = 55 degrees share a common ray, what is the total angle formed?
SolutionTotal angle = 35 + 55 = 90 degrees. This is a Right Angle.

Key Points

  • Acute angle: less than 90 degrees (looks sharp)
  • Right angle: exactly 90 degrees (looks like a square corner)
  • Obtuse angle: between 90 and 180 degrees (looks wide)
  • Two rays meeting at a vertex form an angle measured in degrees
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.An acute angle is:
Explanation: Less than $90^\circ$.
Q2.A right angle is exactly:
Explanation: $90^\circ$.
Q3.An obtuse angle is:
Explanation: $90^\circ$ to $180^\circ$.
Q4.A straight angle is exactly:
Explanation: $180^\circ$.
Practice more MCQs → 📝 Assignment · 35 marks