Angles and Measurement — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A half turn is 90° because you turn halfway around.
Corrected: A half turn is 180° because you face the opposite direction.
The corrected sentence is: "A half turn is 180° because you face the opposite direction." The error was wrong degree measure for half turn: the original sentence "A half turn is 90° because you turn halfway around." needed to be fixed.
2. Fix the sentence:
A full rotation measures 180° because you spin all the way around.
Corrected: A full rotation measures 360° because you spin all the way around back to the start.
The corrected sentence is: "A full rotation measures 360° because you spin all the way around back to the start." The error was wrong degree measure for full turn: the original sentence "A full rotation measures 180° because you spin all the way around." needed to be fixed.
3. Fix the sentence:
An angle of 170° is a right angle because it is close to 180°.
Corrected: An angle of 170° is an obtuse angle because it is greater than 90° but less than 180°.
The corrected sentence is: "An angle of 170° is an obtuse angle because it is greater than 90° but less than 180°." The error was confused right and obtuse: the original sentence "An angle of 170° is a right angle because it is close to 180°." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A quarter turn equals 90 degrees.
A full turn is 360°, and one quarter of 360° is 90°, so a quarter turn equals 90°.
2. A three-quarter turn equals 270 degrees.
Three quarters of a full 360° turn is 270° because 360 × 3/4 = 270.
3. The hands of a clock at 6:00 form a straight angle.
At 6:00 the hour and minute hands point in exactly opposite directions, creating a straight angle of 180°.
4. When you open a door halfway, it turns about 90 degrees.
A door swings from the wall in a quarter-circle arc, so opening it halfway makes a right angle of about 90°.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How many quarter turns does it take to make a full rotation? Explain why.
Sample answer: It takes four quarter turns because each quarter turn is 90° and 4 times 90° equals 360°, which is a full rotation.
A good answer includes: It takes four quarter turns because each quarter turn is 90° and 4 times 90° equals 360°, which is a full rotation.
2. Give an example of an obtuse angle you can see at home and estimate its measure.
Sample answer: A reclining chair leaned back forms an obtuse angle of about 120° between the seat and the backrest.
A good answer includes: A reclining chair leaned back forms an obtuse angle of about 120° between the seat and the backrest.