Measuring and Classifying Angles

How far open is it? That's the whole question.

🧱 See It

Picture a door on a hinge. Push it open just a crack, and the gap between the door and the wall is small. Push it open halfway, and the gap is bigger. Push it all the way until it lies flat back against the wall, and the gap is as wide as it can possibly get — a perfectly straight line.

An angle is just that gap: how far something has been opened, measured in degrees. A book opened a sliver, opened to a right angle like an "L", or opened flat on the table are all the same idea — only the amount of opening changes.

✏️ Draw It

Every angle has a vertex (the hinge point) and two rays (the two edges of the opening). Here are five openings, from barely-cracked to bent-back-past-flat:

40°

Acute angle — about 40°. A narrow, barely-open gap.

90°

Right angle — exactly 90°. A perfect square corner.

130°

Obtuse angle — about 130°. Wider than a square corner, but not flat.

180°

Straight angle — exactly 180°. The door is flat against the wall — both rays form one straight line.

A reflex angle is trickier to draw: the two straight rays alone look just like a smaller angle from the other side. What makes it reflex is which opening you're measuring — the shaded region below shows the wide way around, not the narrow gap left over:

250°

Reflex angle — about 250°. The shaded wedge is the angle being measured: more than half a full turn, wider than a straight line. The small unshaded gap left over is only 110° — a completely different angle from the one being asked about.

🔢 Write It

Once you measure the opening in degrees, it sorts into exactly one of five named categories:

CategoryDegree rule
Acuteless than 90°
Rightexactly 90°
Obtusebetween 90° and 180°
Straightexactly 180°
Reflexmore than 180°
Two boundaries do all the work: 90° splits acute from obtuse, and 180° splits obtuse from reflex.

💡 Worked Examples

Example 1 — Classify 35°

  1. Is it less than 90°? Yes.
  2. Answer: Acute

Example 2 — Classify 90°

  1. Is it exactly 90°? Yes.
  2. Answer: Right

Example 3 — Classify 120°

  1. Is it less than 90°? No. Is it exactly 90°? No.
  2. Is it between 90° and 180°? Yes.
  3. Answer: Obtuse

Example 4 — Classify 180°

  1. Is it exactly 180°? Yes.
  2. Answer: Straight

Example 5 — Classify 250°

  1. Is it more than 180°? Yes.
  2. Answer: Reflex

🧠 Quick Reference

Angle RangeName
Less than 90°Acute
Exactly 90°Right
Between 90° and 180°Obtuse
Exactly 180°Straight
More than 180°Reflex
Acute angles are cute and small. Obtuse angles are big and slow (obtuse sounds like "obese").
👪 For Parents & Tutors

BC Curriculum (Level 1 / Grade 6, Measurement): "Angle measurement and classification."

Watch for: The vocabulary itself — acute, obtuse, reflex — has no inherent memory hook and is easy to mix up under working-memory load; there's nothing about the sound of "obtuse" that says "big" unless you're told the trick. Lean on the mnemonic in Quick Reference, and always have him sketch the angle rather than trying to classify a bare number in the abstract — the picture carries the meaning that the word alone doesn't.

Comes up again: This resurfaces directly in Level 1's own Transformations page, where rotation amounts are described in degrees, and again in Level 3 (Grade 8) Pythagorean theorem and broader geometry work.