Section B Practice Problems

Problem 1

A

B

  1. Write 2 statements that compare the sizes of Angles A and B.
  2. Draw an Angle C that is greater than Angle B.
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Solution
Sample responses:
  1. Angle A is smaller than a square corner, and Angle B is larger than a square corner. Angle B is more open than Angle A.
  2. Sample response:

Sample response. Angle C

Problem 2

A

B

  1. Which set of clock hands makes a greater angle? Explain how you know.
  2. Choose one of the clocks. Describe how to draw the angle represented by the hands on the clock.

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Solution
  1. B, because the minute hand moved 1 number, from 12 to 1, but the hour hand moved more than 2 numbers, from 3 to past 5.
  2. For Clock A, if I start with both hands pointing toward 12, then this angle is made by moving the hour hand from 12 down to 3. 

Problem 3

This angle has a measure of 10∘10^\circ.

 
  1. How many of these angles can you put together, without overlaps, to make a complete circle? Explain or show how you know.
  2. Explain how you can use the given angle to sketch a 5∘5^\circ angle.
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Solution
  1. 36, because there are 360 degrees in the full circle and that is 36×1036 \times 10. 
  2. I can try to cut the 10∘10^\circ in half, and then each of those angles would be 5∘5^\circ. 

2 rays at a point to form an angle. 

Problem 4

Use the given protractor to find the measurement of each angle.


  1. protractor measuring an angle. Left side at 0 or 1 hundred 80 degrees. Right side at 27 or 1 hundred 53 degrees.

  2. protractor measuring an angle. Left side at 45 or 1 hundred 35 degrees. Right side at 1 hundred 80 or 0 degrees.

  3. protractor measuring an angle. Left side at 60 or 1 hundred 20 degrees. Right side at 1 hundred 40 or 40 degrees.
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Solution
  1. 27∘27^\circ
  2. 135∘135^\circ
  3. 80∘80^\circ

Problem 5

Which of these shapes have segments that are perpendicular to one another? Trace or circle the perpendicular segments.

image of 3 geometric shapes.
image of 3 geometric shapes. A. shape with 4 sides of equal length, 2 acute angles and 2 obtuse angles. B. 6 sided shape, looks like a top hat, 1 right angle formed by the top side and left side. C. shape with 4 sides, 1 right angle formed by the top side and right side.

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Solution

B and C. There is one pair of perpendicular segments in B and one pair in C. 

shapes

Problem 6

Draw a ray. How many different 35∘35^\circ angles can you make using your ray and another ray? Explain your reasoning and draw the angles.

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Solution

Sample response: I can make two different 35∘35^\circ angles because I can make an angle in two different directions.

2 angles

Problem 7

What is the smallest angle you can draw?

  1. Can you draw a 10∘10^\circ angle?
  2. Can you draw a 5∘5^\circ angle or a 1∘1^\circ angle?
  3. What is difficult about drawing a small angle?
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Solution
Sample response:
  1. Drawing of a 10∘10^\circ angle
  2. Drawing of a 5∘5^\circ angle
  3. I had trouble drawing a 1∘1^\circ angle because my two rays looked like they were the same. If I had a really big protractor, then the markings for the angles might be further apart, but then it would also be hard to draw the sides of the angle because they would be long.

Problem 8

  1. What is the measurement of each angle on the pentagon?
  2. Connect each vertex to every other vertex with line segments that cross the pentagon. What do you notice? What do you wonder? ​​​​​​

pentagon. each angle equal, each side length equal.

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Solution
  1. Sample response: 108∘108^\circ
  2. Students may notice:
    • The segments make a star shape and many triangles.
    • There is another pentagon in the middle.
    Students may wonder:
    • Is the smaller pentagon the same shape as the larger pentagon?
    • Can I continue doing the same thing to get more and more pentagons?
    • What are the measurements of the angles on all the triangles? Are some of them the same?
pentagon

Problem 9

Can you estimate or find the measurement of Angle F? If so, explain or show how you know.

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Solution

Sample response: About 67∘67^\circ. I know it is greater than 45∘45^\circ and less than 90∘90^\circ. I can fit one 45∘45^\circ angle plus about half of a 45∘45^\circ angle in Angle F (about 45+2245 + 22).