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Angles Unlimited
An Investigative Approach
Materials Needed:
Spaghetti, straws, pencils or Wicki Stix 4”-6” long
Protractors
Paper
Pencils
1. Give each student three pieces of dry spaghetti (straws, pencils or Wicki Stix), a
protractor, sheet of paper and a pencil. Ask students to place the sheet of paper on
his/her desk. Instruct the students to place one of the pieces of spaghetti horizontally
upon the paper. Instruct the students to take a second piece of spaghetti and place it so
that it is in a vertical position and touching the first piece of spaghetti on its left endpoint.
Inform the students that the two pieces of spaghetti represent rays with the same
endpoint. The piece placed horizontally represents a ray going infinitely far to the right,
and the piece placed vertically represents a ray going infinitely far upwards. Ask the
students what they know about the figure that they formed. The two rays intersecting at
the same point form an angle. The rays are the sides of the angle and the common
endpoint is the vertex of the angle. The angle formed is a right angle. Protractors are
used to measure angles. The units used in measuring angles are degrees, minutes and
seconds. In Geometry, we usually measure angles to the nearest degree. Draw the
angle that you have formed, on your paper and measure it with your protractor. Make
sure you place the center of the protractor on the vertex of your angle and line up the
horizontal piece of spaghetti with 0º on the protractor scale. What is the measure of your
angle?
2. A right angle is 90º. If an angle appears smaller than a right angle, we will use the
smaller number on the protractor scale. If an angle appears larger than 90º, we will use
the larger number on the protractor scale.
3. Let the piece of spaghetti that is horizontal, remain in the same position. Rotate the other
piece of spaghetti clockwise. Draw the new angle on your paper and measure it with
your protractor. The two pieces of spaghetti form an acute angle. An acute angle has a
measure greater than 0º and less than 90º. Did your angle measure fall between these
two numbers?
4. With the horizontal piece of spaghetti in the same position, rotate the second piece of
spaghetti to the left passing through the vertical position. Draw the new angle on your
paper and measure it with your protractor. An obtuse triangle has a measure greater
than 90º but less than 180º. Did your angle fall between these two measures?
5. With the horizontal piece of spaghetti in the same position, rotate the second piece of
spaghetti to the left until it forms a straight line with the first piece of spaghetti. Draw this
new angle on your paper and measure it. This is called a straight angle. Its measure is
180º.
6. With the two pieces of spaghetti in the same position, place the third piece of spaghetti at
the vertex, where the two pieces meet. Draw this figure on your paper and measure the
two angles formed. Add these two angle measurements together. What do you get?
These two angles are adjacent supplementary angles and are known as a linear pair
of angles because they are a pair of angles that form a line. Adjacent angles are two
angles who share a common endpoint, a common side and no common interior points.
Supplementary angles are two angles whose sum of their measures equal 180º.
7. Conclusion. Discuss with the students that angles are a part of their daily lives. Ask
students where they might find angles in the real world. Examples may include: the
building of streets and buildings, the path that an airplane takes when taking off, etc.
8. This experiment gives students a visual appreciation of geometric vocabulary with
respect to angles.
Geometry in the Trees
Angles Unlimited
An Investigative Approach (Suggested Answers)
Materials Needed:
Spaghetti, straws, pencils or Wicki Stix 4”-6” long
Protractors
Paper
Pencils
1. Give each student three pieces of dry spaghetti (straws, pencils or Wicki Stix), a
protractor, sheet of paper and a pencil. Ask students to place the sheet of paper on his/her
desk. Instruct the students to place one of the pieces of spaghetti horizontally upon the
paper. Instruct the students to take a second piece of spaghetti and place it so that it is in a
vertical position and touching the first piece of spaghetti on its left endpoint. Inform the
students that the two pieces of spaghetti represent rays with the same endpoint. The piece
placed horizontally represents a ray going infinitely far to the right, and the piece placed
vertically represents a ray going infinitely far upwards. Ask the students what they know
about the figure that they formed. The two rays intersecting at the same point form an angle.
The rays are the sides of the angle and the common endpoint is the vertex of the angle.
The angle formed is a right angle. Protractors are used to measure angles. The units used
in measuring angles are degrees, minutes and seconds. In Geometry, we usually measure
angles to the nearest degree. Draw the angle that you have formed, on your paper and
measure it with your protractor. Make sure you place the center of the protractor on the
vertex of your angle and line up the horizontal piece of spaghetti with 0º on the protractor
scale. What is the measure of your angle? (Answers will vary, check student’s drawings
and measurements)
2. A right angle is 90º. If an angle appears smaller than a right angle, we will use the
smaller number on the protractor scale. If an angle appears larger than 90º, we will use the
larger number on the protractor scale.
3. Let the piece of spaghetti that is horizontal, remain in the same position. Rotate the other
piece of spaghetti clockwise. Draw the new angle on your paper and measure it with your
protractor. The two pieces of spaghetti form an acute angle. An acute angle has a measure
greater than 0º and less than 90º. Did your angle measure fall between these two
numbers? (yes)
4. With the horizontal piece of spaghetti in the same position, rotate the second piece of
spaghetti to the left passing through the vertical position. Draw the new angle on your paper
and measure it with your protractor. An obtuse triangle has a measure greater than 90º but
less than 180º. Did your angle fall between these two measures? (yes)
5. With the horizontal piece of spaghetti in the same position, rotate the second piece of
spaghetti to the left until it forms a straight line with the first piece of spaghetti. Draw this new
angle on your paper and measure it. This is called a straight angle. Its measure is 180º.
6. With the two pieces of spaghetti in the same position, place the third piece of spaghetti at
the vertex, where the two pieces meet. Draw this figure on your paper and measure the two
angles formed. Add these two angle measurements together. What do you get? 180.
These two angles are adjacent supplementary angles and are known as a linear pair of
angles because they are a pair of angles that form a line. Adjacent angles are two angles
who share a common endpoint, a common side and no common interior points.
Supplementary angles are two angles whose sum of their measures equal 180º.
7. Conclusion. Discuss with the students that angles are a part of their daily lives. Ask
students where they might find angles in the real world. Examples may include: the building
of streets and buildings, the path that an airplane takes when taking off, etc.
8. This experiment gives students a visual appreciation of geometric vocabulary with respect
to angles.