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Math Lesson: Angles
Grade Level: 7
Lesson Summary: Students reason through creating acute, obtuse, complementary, supplementary,
interior, exterior, and vertical angles. They draw a triangle and calculate the sum of the exterior angles.
Advanced students play a Twenty Questions game to identify particular shapes with specific angle
measurements. Struggling students calculate the measurements of complementary, supplementary and
vertical angles.
Lesson Objectives:
The students will know…

How to differentiate between angle types.
The students will be able to…
 solve simple equations for an unknown angle in a figure.
 construct triangles
 calculate angle sums of triangles
Learning Styles Targeted:
Visual
Auditory
Kinesthetic/Tactile
Pre-Assessment:
Determine whether students understand the differences between acute, right, obtuse, straight, and
reflex angles.
1) Draw each type of angle on the board, and ask students to classify and estimate the measure of
each angle.
2) Identify students who do not understand the differences.
Whole-Class Instruction
Materials Needed: Protractors, color pencils
Procedure:
Presentation
1) Point to an analog clock or draw one on the board. Ask how many degrees the hour hand has
rotated when it travels from 12:00 to 12:00 or 3:00 to 3:00 (360). Identify the fractions of a
complete rotation (From 12 to 6=180 degrees; from 12 to 3= 90 degrees; from 12 to 1= 30
degrees; from 12:00 to 12:01=6 degrees).
2) Instruct students to use their protractors to measure and draw an acute angle and an obtuse
angle. Students compare their angles to an object (piece of paper or a book) with a 90 degree
angle.
3) Next, draw perpendicular lines to make four right angles, an x and y axis. Ask what type of angles
you have created. (4 right angles)
4) Then draw a diagonal line through the figure to create 60- and 30-degree angles. Label each angle
with letters to describe the angles (ACF for example). Explain that when the measurement of two
angles adds to 90 degrees (a right angle), they are complementary. Have students use color
pencils construct 2 complementary angles. Students can create a legend to identify the
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complementary angles with the appropriate color.
5) Explain that two angles are adjacent when they have a common side and common vertex (center
point). Ask if complementary angles are adjacent. (yes)
6) Explain that two angles are supplementary if their sum is 180 degrees. Have students use color
pencils to identify two supplementary angles and add those to the legend, labeling them with
letters.
7) Explain that angles formed by two intersecting straight lines and are opposite each other are called
vertical angles. Have students use another color to identify two vertical angles and add that to the
legend. Ask if vertical angles have equal measure (yes) and explain when angles are equal, they
are congruent.
Guided Practice
8) Next instruct students to draw a line parallel to the x-axis that intersects the other lines to create
triangles. Explain that a line that crosses other lines is a transversal.
9) Students use a color pencil to identify an interior angle (inside a triangle) and an exterior angle,
(outside a triangle) and add those to the legend. Ask students to determine the sum of the interior
angle measurements. (180 degrees, which forms a straight angle).
10) Students measure each angle in any triangle they have created and add the measurements
together. Confirm that the sum of every triangle’s interior angles measures 180 degrees. Ask
students to generalize the sum of a triangle’s exterior angles measurements.
Independent Practice
11) Students draw a triangle with interior angles of 90, 45, and 45 degrees.
12) Instruct students to extend each side of the triangle to three exterior angles. Have them calculate
the measurements of each of the exterior angles they created, and then add the sum of all the
exterior angle measurements. (360)
13) Students hypothesize whether the sum of exterior angles would always be the same if the interior
angle measurements were 60, 60, and 60 and explain why.
Closing Activity
14) Students explain the significance of the numbers 360, 180, and 90 as they relate to angles and
triangles.
15) Ask students how to determine the measurement of a vertical, complementary, or supplementary
angle if you know one angle measurement.
Advanced Learner
Materials Needed: Protractor
Procedure:
Break students into pairs to play this game.
1) One person draws a figure (any type of triangle or quadrilateral) and measure its angles so that no
one else can see it.
2) The other players takes a turn asking a question, such as, “Does your figure have a total of 180
degree interior angles?” until the figure with the correct angle measurements is named.
3) Have students explain their results and strategies.
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Struggling Learner
Materials Needed: Protractor
Procedure:
1) Students draw each of the following angles and then calculate the complementary, supplementary,
and vertical angle measurements: 30, 45, 60, 85. (complementary: 60, 45, 30, 5; supplementary:
150, 135, 120, 95; and vertical 30, 45, 60, 85) Students should work independently.
2) Describe their results and explain their reasoning. Then students complete the independent
practice activity.
*see supplemental resources
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