Section B: Practice Problems The Size of Angles

Section Summary

Details

In this section, we learned about ways to describe and measure the size of angles.

We used clocks to describe angles as a turn of one away from the other. We learned that a degree is a measure of the turn around a circle and that 1 degree is ​​​​ of a full turn of a ray through a circle.

Finally, we learned that a protractor is a tool used to measure angles and can also be used to create angles of a certain measure.

protractor


A protractor has two sets of numbers and that either set of numbers could be used, but it is helpful to use the set that counts up from 0 rather than count down from 180. We used a protractor to measure and draw different angles.

Problem 1 (Lesson 6)

A
angle formed by two rays
B
angle formed by two rays

  1. Write two statements that compare the size of angles A and B.

  2. Draw an angle C that is bigger than both angle A and angle B.

Problem 2 (Lesson 7)

A
clock showing 3:00
B
clock showing 5:05

  1. Which set of clock hands make a greater angle? Explain how you know.

  2. Choose one of the clocks and describe how to use the clock to draw the angle represented by the hands on the clock.

Problem 3 (Lesson 8)

This angle has a measure of .

angle formed by two rays
 

  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 angle.

Problem 4 (Lesson 9)

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.

Problem 5 (Lesson 10)

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

image of 3 geometric shapes.

Problem 6 (Lesson 11)

Draw a ray. How many different angles can you make using your ray and another ray? Explain your reasoning and make the angles.

Problem 7 (Exploration)

What is the smallest angle you can draw?

  1. Can you draw a angle?

  2. What about a angle or a angle?

  3. What is difficult about drawing a small angle?

Problem 8 (Exploration)

pentagon. each angle equal, each side length equal.

  1. What are the measurements of the angles on the pentagon?

  2. Connect every pair of vertices of the pentagon with a line segment. What do you notice? What do you wonder?

Problem 9 (Exploration)

Exploration

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

image of a kite. The angle located on the far right below the horizontal cross is labeled f.