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Math 102 Handout #3: Angles and Their Properties, Assignments of Mathematics

This document from math 102, spring 2007, covers various angle-related problems and exercises. Students are asked to determine the size of different angles using a protractor, find complementary, supplementary, and vertical angles, and explore the relationship between perpendicular lines through folding. Dr. Howald's handout also includes examples of acute, obtuse, and right angles.

Typology: Assignments

Pre 2010

Uploaded on 08/09/2009

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Math 102 Handout # 3 Spring 2007
Dr. Howald 3-Angles.doc
1. Which of the following angles is bigger? How would you explain the answer to a
student in third grade? Measure each with your protractor to the nearest degree.
2. Consider a clock (correctly set) that starts ticking at noon.
a. What is the measure of the total angle swept by the hour hand when it reaches 3:00
P.M.?
b. What is the angle between the hour hand and minute hand at exactly 4:00 A.M.?
c. At what hour(s) will the angle between the hour and minute hands be exactly 30?
3. In the figure to the right, assume the lines DH and AF are perpendicular. Find angles,
written in the form AFG, which have the following properties:
a. complementary angles.
b. supplementary angles.
c. vertical angles.
d. adjacent angles that are not complementary
or supplementary.
e. an acute angle.
f. an obtuse angle.
g. a right angle.
4. Using a clean sheet of paper (with no holes or rips) follow these steps.
Fold one corner of the sheet (at an angle) on to the paper and crease it so the line
created will show when the paper is unfolded. (Do not unfold it.)
E
A
F
G
B
H
C
D
pf2

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Math 102 Handout # 3 Spring 2007

Dr. Howald 3-Angles.doc

  1. Which of the following angles is bigger? How would you explain the answer to a student in third grade? Measure each with your protractor to the nearest degree.
  2. Consider a clock (correctly set) that starts ticking at noon. a. What is the measure of the total angle swept by the hour hand when it reaches 3: P.M.? b. What is the angle between the hour hand and minute hand at exactly 4:00 A.M.? c. At what hour(s) will the angle between the hour and minute hands be exactly 30?
  3. In the figure to the right, assume the lines DH and AF are perpendicular. Find angles, written in the form AFG, which have the following properties: a. complementary angles. b. supplementary angles. c. vertical angles. d. adjacent angles that are not complementary or supplementary. e. an acute angle. f. an obtuse angle. g. a right angle.
  4. Using a clean sheet of paper (with no holes or rips) follow these steps.  Fold one corner of the sheet (at an angle) on to the paper and crease it so the line created will show when the paper is unfolded. (Do not unfold it.) E A F G B H C D

Math 102 Handout # 3 Spring 2007

Dr. Howald 3-Angles.doc

 Fold any part of the crease you made onto itself, and crease the new line that is formed.  Unfold the paper to see the two creased lines. a. Use your Protractor to measure the angle made by the two creases. b. Explain why two lines formed this way must be perpendicular. c. Try to use folding to create angles of 45, 135, and 2230’. Explain the folding steps for each.