A student holds the corner of a piece of paper against an angle in the room. The angle is wider than the paper's corner. How should the student classify this angle?
AAcute, because it looks like a sharp corner
BRight angle, because it is close to a square corner
CObtuse, because it is wider than 90°
DStraight angle, because it is wider than a right angle
The paper corner is a right angle (exactly 90°). If the angle being tested is wider than the paper corner, it is greater than 90°, which makes it obtuse. An acute angle would be narrower than the paper corner (less than 90°). A straight angle is a flat, 180° line — far wider than an obtuse angle. The paper-corner comparison is exactly the practical test described in the lesson.
Question 2 Multiple Choice
Which of the following angle measures is acute?
A90°
B135°
C65°
D180°
An acute angle measures less than 90°. 65° is the only option below 90°. 90° is a right angle. 135° is obtuse (greater than 90° but less than 180°). 180° is a straight angle. Knowing the reference points — 0°, 90°, 180° — lets you classify any angle by comparison.
Question 3 True / False
An obtuse angle measures more than 90° but less than 180°.
TTrue
FFalse
Answer: True
This is the precise definition: obtuse angles sit between a right angle (90°) and a straight angle (180°). They look 'blunt' or spread out compared to a square corner. Angles at exactly 90° are right angles, and anything above 180° would be a reflex angle (not typically covered at this level). Knowing the boundaries — acute below 90°, right at 90°, obtuse between 90° and 180° — is the classification system.
Question 4 True / False
A right angle can measure anywhere from about 80° to 100° as long as it looks like a square corner.
TTrue
FFalse
Answer: False
A right angle is exactly 90° — not approximately, not 'close enough.' Precision is the point: the small square symbol drawn at a vertex signals exactly 90°, which is why architects, carpenters, and mathematicians depend on right angles to build and describe the world. An angle that looks like a square corner but measures 88° is acute; one measuring 92° is obtuse. The visual check with a paper corner is a practical approximation, but the definition is exact.
Question 5 Short Answer
How can you use a piece of paper to decide whether an unknown angle is acute, right, or obtuse? Describe the process.
Think about your answer, then reveal below.
Model answer: Hold the corner of a piece of paper (which is a right angle, exactly 90°) against the vertex of the angle you want to classify. If the two sides of the angle align exactly with the sides of the paper corner, the angle is a right angle. If the angle is narrower — its opening fits inside the paper corner — it is acute (less than 90°). If the angle is wider — it opens beyond the paper corner — it is obtuse (greater than 90°). The paper corner works as a portable right-angle reference.
This physical test makes the abstract definition concrete and usable without a protractor. It also reinforces why 90° is the key reference point: all angle classification depends on comparison to a right angle. Students can apply this check to any angle they encounter — in the classroom, at home, or in geometric diagrams — making it a transferable skill, not just a memorized fact.