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:
· Acute angles
1. Angle that measures between 0o and 90o
2. Examples: 30o, 58o, 88o
· Right angles
1. Angle that measures exactly 90o
2. A square in the corner represents it being a right angle
3. Example: (only one) 90o
· Obtuse angles
1. Angle that measures between 90o and 180o
2. Examples: 93o, 175o, 100o
· Straight angles
1. Angle that measures exactly 180o
2. Looks like a straight line
3. Example: (only one) 180o
· Complementary angles
1. Angles added together to equal 90o
2. Example: 30o + 60o = 90o
3. A + B = 90o
· Supplementary angles
1. Angles added together to equal 180o
2. Example: 132o + 48o = 180o
3. A + B = 180o
· 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 (10th – 12th 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 |
19