A student measures what clearly looks like an acute angle and gets a reading of 130° on the protractor. What should she conclude?
AThe angle is obtuse because 130° is between 90° and 180°
BShe has read the wrong scale — the correct reading is 50°
CThe angle is reflex because any reading above 90° means a large angle
DShe needs to re-align the vertex and measure again from scratch
A protractor has two scales that run in opposite directions. If you align the left ray and accidentally read the right-to-left scale, you get the supplement of the correct angle (130° instead of 50°). The error-checking rule is: classify the angle first. An acute angle must be less than 90° — a reading of 130° for an obviously acute angle means you read the wrong scale. The correct reading is 180° − 130° = 50°.
Question 2 Multiple Choice
Two students both draw a 40° angle. One uses short rays; the other uses rays three times as long. Which statement is true?
AThe student with longer rays has a larger angle because the rays extend farther
BBoth angles measure exactly 40° because degrees measure rotation, not the length of the rays
CThe student with longer rays has an angle of 120° (40° × 3)
DIt is impossible to tell which angle is larger without measuring both with a protractor
Degrees measure the amount of rotation between the two rays — the opening between them — not how far the rays extend. A 40° angle is a 40° angle regardless of whether the rays are 1 cm or 1 meter long. This is a fundamental property of angle measurement: ray length is irrelevant. Option A describes the most common misconception, where students confuse physical size on paper with the actual angle measure.
Question 3 True / False
An acute angle measured with a protractor must give a reading less than 90°.
TTrue
FFalse
Answer: True
By definition, an acute angle is smaller than a right angle (90°). So if you measure an angle you have classified as acute and your protractor gives a reading of 90° or more, you have made an error — either in classification or in reading the protractor scale. This is exactly why classifying before measuring is a useful error-checking habit.
Question 4 True / False
Longer rays on an angle indicate a larger angle measurement in degrees.
TTrue
FFalse
Answer: False
Ray length has no effect on degree measurement. Degrees measure the rotation between the rays — the 'opening' of the angle. You can have a tiny 10° angle with very long rays, or a wide 170° angle with very short rays. Students who rely on visual size rather than measuring are often fooled by angles drawn with different ray lengths.
Question 5 Short Answer
Why does a protractor have two sets of numbers (two scales), and how do you decide which scale to read?
Think about your answer, then reveal below.
Model answer: The two scales let you measure angles that open in either direction — one scale reads left to right (0 to 180) and one reads right to left (0 to 180). You read the scale whose 0° mark is aligned with the ray you placed on the baseline. A practical check: classify the angle as acute or obtuse first, then confirm your reading matches — acute readings must be less than 90°, obtuse readings must be between 90° and 180°.
The two-scale design is intentional: it allows you to align either the left or right ray with the baseline and still get a correct reading. The confusion arises because both scales show numbers in the same position — you have to actively choose the right one. The classify-first habit is the best safeguard: if the angle looks acute and you read 140°, you know immediately you've used the wrong scale.