Topic B notes.pdf

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Grade 7 Chapter 7 Page 1

Module 3 Lesson 11

Classify Angles

Angle- formed by 2 rays that share a

common vertex. The symbol is a slanted capitol L.

Vertex- The point where the two rays

meet.

Naming an angle

Method 1: Using a 3 letter name (all capitols) ےBAC 1. Name one point on one ray

2. Name the vertex point

3. Name one point on the other ray

Method 2: Using a 1 letter name (this can only be done when there is only one angle with this vertex in a diagram) ے A

1. Name the vertex point

Method 3: Using a numerical name when the number is inside of the 2 rays. ے 1

Classify Angles

Acute Angle-

An angle with a measure greater than 0 and less than 90.

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Grade 7 Chapter 7 Page 2 Obtuse Angle- An angle that measures larger than 90 but less than 180

(90< measure <180)

Right Angle- An angle that is exactly 90. The two sides are perpendicular to each other. The notch inside tells us it is a right angle.

Congruent- Having the same measure

Vertical Angles- Opposite angles formed by the intersection of 2 lines. The vertical angles are congruent.

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Grade 7 Chapter 7 Page 3 Adjacent Angles - Angles that:

 Have the same vertex (B)

 share a common side (BC)

 do not overlap

To find a missing measure:

1. Figure out what you know about the relationship between the angles :

 are they 2 adjacent angles inside of a right angle and should add up to 90

 are they 2 adjacent angles inside of a straight angle and should add up to 180

 are they vertical angles that are congruent 2. Set up an equation (sum of the parts = whole) 3. Solve the equation

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Complementary and Supplementary Angles

Complementary Angles- Two angles that have a sum of 90

Supplementary Angles- Two angles that have a sum of 180

To find a missing measure:

1. Figure out what you know about the relationship between the angles :

 are the angles complementary and add up to 90

 are the angles supplementary and add up to 180

 are they vertical angles that are congruent 2. Set up an equation (sum of the parts = whole) 3. Solve the equation

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7-3: Triangles

Triangle- A figure with three sides and three angles. The angles have a sum of 180.

To find a missing measure:

1. Figure out what you know about the relationship between the angles:

 are any of the angles right angles, if so it = 90

 are the angles congruent

2. Set up an equation (sum of the angles = 180) 3. Solve the equation

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How to measure with a protractor:

1. Estimate the measure of your angle. Is it greater, less than or equal to 90 degrees?

2. Line up the center of the protractor with the vertex of the angle you want to measure.

3. Line up 1 side of the angle with the baseline of the protractor (0 degrees) so that the rest of the angle is inside the protractor.

4. Follow the numbers, starting with 0 degrees, until you get to the opposite side of the angle. (It might help if you use a ruler to make the sides of the angle longer) This is the measure of your angle. *

*A common error is to use the wrong set of numbers. Make sure your estimate matches your measurement.

Vertex baseline

How to draw an angle with a protractor:

1. Start by drawing a ray (a line with one endpoint). The endpoint will be the vertex of your angle.

2. Line up the center of the protractor with the vertex of the angle you want to draw.

3. Line up the side of the angle with the baseline (0 degrees) of the protractor. 4. Follow the numbers, starting with 0 degrees, until you get to the number of

degrees that you want your angle to be. Mark this spot.

5. Using a ruler, connect the vertex to the mark you just made. *

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1-6 83 67 50 33 17 0

1) 2)

3) 4)

5) 6)

1. 120°

2. 75°

3. 85°

4. 155°

5. 60°

6. 160°

Use a protractor to find the angle shown.

Finding Angles

Math _{www.CommonCoreSheets.com}

Name:

A n s w e r s

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1-6 83 67 50 33 17 0

1) 35° 2) 10°

3) 145° 4) 125°

5) 75° 6) 60°

Use a protractor to complete the angle shown. Creating Angles

Name:

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1-10 90 80 70 60 50 40 30 20 10 0

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 160 17 0 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20

10 15

90

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 160 1 70 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 85 105 90 80 70 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 16 0 17 0

180 0 0

180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 80 160 90 80 70 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 16 0 1 70

180 0 0

180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 60 65

90 80 ₇₀ 60 50 40 30 2₀ 1 0 100 110 120 130 140 150 160 17 0 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 105 ₆₅

90 80 ₇₀ 60 50 40 30 2₀ 1 0 100 110 120 130 140 150 160 1 70 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 125 140

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 160 17 0 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 85 115

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 160 1 70 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 85 115

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 16 0 17 0 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 35 15

90 80 ₇₀ 60 50 40 30 2₀ 1₀ 100 110 120 130 140 150 16 0 1 70 180 0 0 180 100 110 120 13₀ 14₀ 15₀ 1₆ 0 1₇ 0 80 70 60 50 40 30 20 10 85 95 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 1. 75° 2. 20° 3. 80° 4. 5° 5. 40° 6. 15° 7. 30° 8. 30° 9. 20° 10. 10°

Use the protractor to determine each angle.

Determining Angles with Protractors

Name:

A n s w e r s

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1-10 95 90 85 80 75 70 65 60 55 50 11-20 45 40 35 30 25 20 15 10 5 0

1) 161° Obtuse

2) 153° Obtuse

3) 17° Acute

4) 88° Acute

5) 131° Obtuse

6) 90° Right

7) 38° Acute

8) 79° Acute

9) 174° Obtuse

10) 90° Right

11) 112° Obtuse

12) 50° Acute

13) 45° Acute

14) 14° Acute

15) 145° Obtuse

16) 107° Obtuse

17) 23° Acute

18) 133° Obtuse

19) 180° Straight

20) 83° Acute

1. Obtuse 2. Obtuse 3. Acute 4. Acute 5. Obtuse

6. Right 7. Acute 8. Acute 9. Obtuse 10. Right 11. Obtuse

12. Acute 13. Acute 14. Acute 15. Obtuse 16. Obtuse 17. Acute

18. Obtuse 19. Straight 20. Acute

Determine if the angle described is 'acute', 'obtuse','right' or 'straight'. Finding Angles By Degrees

Name:

A n s w e r s

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Name:

A n s w e r s

1-9 89 78 67 56 44 33 22 11 0

1)

B A

C

Which choice best

represents ∟ABC?

A. 29° B. 101° C. 68° D. 131° 2) L K M

Which choice best

represents ∟KLM?

A. 90° B. 147° C. 15° D. 175° 3) L K M

Which choice best

represents ∟KLM?

A. 90° B. 33° C. 128° D. 180° 4) B A C

Which choice best

represents ∟ABC?

A. 90° B. 176° C. 49° D. 152° 5) L K M

Which choice best

represents ∟KLM?

A. 26° B. 114° C. 71° D. 177° 6) L K M

Which choice best

represents ∟KLM?

A. 127° B. 149° C. 103° D. 56° 7) L K M

Which choice best

represents ∟KLM?

A. 57° B. 168° C. 4° D. 95° 8) L K M

Which choice best

represents ∟KLM?

A. 102° B. 8° C. 31° D. 153° 9) B A C

Which choice best

represents ∟ABC?

A. 13° B. 152° C. 49° D. 109° 1. D 2. A 3. D 4. C 5. B 6. D 7. A 8. D 9. A Estimating Angle Solve each problem.