3B · Chapter 12 · Lesson 3
Right Angles
Identify right, acute, and obtuse angles using a square corner.
Today's mathematical question
An angle measures exactly 90°. Is it acute, right, or obtuse?
Learning target
Identify right, acute, and obtuse angles using a square corner.
Before starting: Prior lesson: Angles. 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
An angle measures 142°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 142° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 142 degrees; angle size depends on rotation, not ray length. - P2
An angle measures 63°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 63° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 63 degrees; angle size depends on rotation, not ray length. - P3
An angle measures 47°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 47° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 47 degrees; angle size depends on rotation, not ray length.
Learn and understand
A right angle is one quarter of a full turn, or 90 degrees. An acute angle is smaller; an obtuse angle is greater than a right angle but smaller than a straight angle. Compare with the corner of a square instead of trusting how the picture is tilted. A corner of ordinary rectangular paper forms a 90-degree angle. Rotate the paper; the angle stays 90 degrees. Compare a smaller and a larger opening against that benchmark.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Lay a square corner at the vertex, aligning one side with a ray. Decide whether the other ray falls inside, matches, or extends beyond the right-angle opening.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- right angle
- 90-degree turn
- acute angle
- between 0 and 90 degrees
- obtuse angle
- between 90 and 180 degrees
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
An angle measures exactly 90°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- An exact quarter-turn measures 90° and forms a right angle. Acute angles are smaller; obtuse angles are larger.
- Check that the answer uses the right units and makes sense.
Answer: right
Check your understanding 1
An angle measures 13°. Is it acute, right, or obtuse?
Reveal answer and explanation
acute — Compare 13° 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 121°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- Compare 121° 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 2
An angle measures 123°. Is it acute, right, or obtuse?
Reveal answer and explanation
obtuse — Compare 123° 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 160°. Is it acute, right, or obtuse?
- Identify the whole, the units, and what the question asks.
- Compare 160° 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 57°. Is it acute, right, or obtuse?
Reveal answer and explanation
acute — Compare 57° 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 161°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 161° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 161 degrees; angle size depends on rotation, not ray length. - G2
An angle measures 90°. Is it acute, right, or obtuse?
Reveal explanation
Answer: right
Compare 90° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 90 degrees; angle size depends on rotation, not ray length. - G3
An angle measures 162°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 162° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 162 degrees; angle size depends on rotation, not ray length. - G4
An angle measures 78°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 78° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 78 degrees; angle size depends on rotation, not ray length. - G5
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.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
An angle measures 110°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 110° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 110 degrees; angle size depends on rotation, not ray length. - I2
An angle measures 33°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 33° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 33 degrees; angle size depends on rotation, not ray length. - I3
An angle measures 45°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 45° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 45 degrees; angle size depends on rotation, not ray length. - I4
An angle measures 125°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 125° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 125 degrees; angle size depends on rotation, not ray length. - I5
An angle measures 95°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 95° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 95 degrees; angle size depends on rotation, not ray length. - I6
An angle measures 133°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 133° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 133 degrees; angle size depends on rotation, not ray length. - I7
An angle measures 137°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 137° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 137 degrees; angle size depends on rotation, not ray length. - I8
An angle measures 107°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 107° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 107 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 60°. A student calls it obtuse because the rays look long. Explain the error.
Reveal explanation
Answer: Acute
60° 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 163°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 163° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 163 degrees; angle size depends on rotation, not ray length. - E2
An angle measures 65°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 65° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 65 degrees; angle size depends on rotation, not ray length. - E3
An angle measures 68°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 68° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 68 degrees; angle size depends on rotation, not ray length.