3B · Chapter 12 · Lesson 2
Angles
Recognize angles as turns and compare their size independent of arm length.
Today's mathematical question
An angle measures 117°. Is it acute, right, or obtuse?
Learning target
Recognize angles as turns and compare their size independent of arm length.
Before starting: Prior lesson: Circles. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
A circle has diameter 6 cm. What is its radius?
Reveal explanation
Answer: 3 cm
The radius is half the diameter. 6 ÷ 2 = 3 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - P2
A circle has radius 22 cm. What is its diameter?
Reveal explanation
Answer: 44 cm
A diameter joins two radii end to end through the center: 22 + 22 = 44 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - P3
A circle has diameter 56 cm. What is its radius?
Reveal explanation
Answer: 28 cm
The radius is half the diameter. 56 ÷ 2 = 28 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
Learn and understand
An angle describes an amount of turning between two rays meeting at one vertex. A longer arm does not make a larger angle when the turn stays unchanged. Think of opening a door: the angle changes when the direction of the door changes, not when the door gets longer. Open a book slightly and then much wider. The opening angle increases even if its covers keep the same length. An angle measures the amount of turn, not how long the lines are.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Use two strips joined at one end and rotate one strip. Trace the same angle using both short and long strips.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- angle
- turn between two rays
- vertex
- common endpoint of rays
- ray
- straight path starting at a point
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
An angle measures 117°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- Compare 117° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
- Check that the answer uses the right units and makes sense.
Answer: obtuse
Check your understanding 1
An angle measures 24°. Is it acute, right, or obtuse?
Reveal answer and explanation
acute — Compare 24° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Worked example 2
Explore, calculate, verify
An angle measures 89°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- Compare 89° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
- Check that the answer uses the right units and makes sense.
Answer: acute
Check your understanding 2
An angle measures 137°. Is it acute, right, or obtuse?
Reveal answer and explanation
obtuse — Compare 137° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Worked example 3
Explore, calculate, verify
An angle measures 166°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- Compare 166° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
- Check that the answer uses the right units and makes sense.
Answer: obtuse
Check your understanding 3
An angle measures 19°. Is it acute, right, or obtuse?
Reveal answer and explanation
acute — Compare 19° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
An angle measures 159°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 159° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 159 degrees; angle size depends on rotation, not ray length. - G2
An angle measures 145°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 145° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 145 degrees; angle size depends on rotation, not ray length. - G3
An angle measures 49°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 49° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 49 degrees; angle size depends on rotation, not ray length. - G4
An angle measures 122°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 122° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 122 degrees; angle size depends on rotation, not ray length. - G5
An angle measures 48°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 48° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 48 degrees; angle size depends on rotation, not ray length.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
An angle measures 34°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 34° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 34 degrees; angle size depends on rotation, not ray length. - I2
An angle measures 164°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 164° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 164 degrees; angle size depends on rotation, not ray length. - I3
An angle measures 40°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 40° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 40 degrees; angle size depends on rotation, not ray length. - I4
An angle measures 141°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 141° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 141 degrees; angle size depends on rotation, not ray length. - I5
An angle measures 156°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 156° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 156 degrees; angle size depends on rotation, not ray length. - I6
An angle measures 54°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 54° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 54 degrees; angle size depends on rotation, not ray length. - I7
An angle measures 109°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 109° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 109 degrees; angle size depends on rotation, not ray length. - I8
An angle measures 105°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 105° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 105 degrees; angle size depends on rotation, not ray length.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
One ray of an angle is made longer without rotating either ray. Does the angle change?
Reveal explanation
Answer: No
Angle size depends on the turn between rays, not on how long they are drawn.
- C2
An angle is 65°. A student calls it obtuse because the rays look long. Explain the error.
Reveal explanation
Answer: Acute
65° is below 90°, so the angle is acute; ray length is irrelevant.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
An angle measures 62°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 62° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 62 degrees; angle size depends on rotation, not ray length. - E2
An angle measures 103°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 103° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 103 degrees; angle size depends on rotation, not ray length. - E3
An angle measures 101°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 101° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 101 degrees; angle size depends on rotation, not ray length.