Goal:  My students will be introduced to many types of angles.  They will be shown how to find the measurements of certain angles.

 

Objective:  The students will be able to identify, define, estimate, measure angles (such as acute, right, obtuse, straight, complementary, supplementary, adjacent, vertical, and congruent).

 

Mind Set:  Angles are seen in just about everything.  Some people that use angles in their work are Architects and Constructors.

 

Lesson:

1. I will ask the class to tell me everything that they know about angles.  I want to know all of the characteristic and measurements and anything else that you might know about them.  I will write these down on the board.
2. I will teach the different kinds of angles and the characteristics of them. (use transparencies)

 

 

·        Acute angles

1.      Angle that measures between 0^o and 90^o

2.      Examples: 30^o, 58^o, 88^o

 

 

 

·        Right angles

1.      Angle that measures exactly 90^o

2.      A square in the corner represents it being a right angle

3.      Example: (only one) 90^o

 

 

 

·        Obtuse angles

1.      Angle that measures between 90^o and 180^o

2.      Examples: 93^o, 175^o, 100^o

 

 

 

·        Straight angles

1.      Angle that measures exactly 180^o

2.      Looks like a straight line

3.      Example: (only one) 180^o

 

 

 

·        Complementary angles

1.      Angles added together to equal 90^o

2.      Example: 30^o + 60^o = 90^o

3.      A + B = 90^o

 

 

 

·        Supplementary angles

1.      Angles added together to equal 180^o

2.      Example: 132^o + 48^o = 180^o

3.      A + B = 180^o

 

 

 

·        Adjacent angles

1.      Angles that share a common side and a common vertex

2.      Do not have to be equal in measure but sometimes will be

3.      A and B are adjacent angles but not congruent

 

 

 

·        Vertical angles

1.      Angles that are opposite from one another

2.      Vertical angles will have the same measures

3.      A = B

 

 

 

·        Congruent angles

1.      Angles that have the same measure

2.      A B

 

 

 

 

 

 

3.  Here are some examples in finding the measures of the angles.  (See below)

 

 

Closure:  Review the different types of angles by showing a picture of an angle and letting the students identify the angle type.  I will also answer any questions that they might have.

 

Evaluation:  (Due tomorrow)  List 5 examples of each type of angle (acute, right, obtuse, and straight) that you find out in the world.

 

Grade Level:  High school Geometry class (10^th – 12^th Graders)

 

 

 

 

 

 

Practice Problems:  Directions:  Find the measures of the following angles.  (Answers in red and in degree measurements.)

 

 

1)  These angles are complementary.

 

 

 

 

 

 

 

 

x + 4 + 2x – 10 3x – 6 3x x

= = = =

90 90 96 32

 

 

 

 

 

2)

 

 

 

 

 

 

 

 

2 (x + 10) + 3x + 10 2x + 20 + 3x +10 5x + 30 5x x

= = = = =

180 180 180 150 30

 

 

 

 

3)

 

 

3x + 5 + x 4x + 5 4x x

= = = =

125 125 120 30

 

 

 

 

 

 

 

 

 

 

 

4)  Find the 3 remaining angles. (X, Y, Z)

 

Y

=

98

since W and Y are vertical angles, they are equal

 

 

180 – 92 82

= =

X X

X and Z are also vertical angles therefore they are equal

 

 

 

 

 

5)  Solve for x.

 

 

2x – 5 2x x

= = =

35 40 20

 

              X = 20

 

 

 

 

 

 

 

 

 

6)

 

 

 

4x – 17 3x x

= = =

X + 10 27 9

 

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