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Unit 10

Angles

Name:

Teacher:

Grade:

2

Lesson 1 Classwork

Complementary Angles

Complementary Angles:

** Using the above definition, the word sum tells us that we are using addition to set up an equation. The

word is tells us that the total is 90 degrees. **

Complementary angles do not have to be adjacent (next to each other) for them to be complementary.

Notice in the diagram below to the left, when complementary angles are adjacent to each other, they form a

right angle. Below to the right, they are still complementary, just not adjacent to each other. What this

means is: <1 + <2 = 90

1. Complementary Angles are two angles whose sum is _.

2. Complementary angles form what type of angle? .

3. The outer rays of complementary angles are to each other.

4. What is the complement of a 40 degree angle? .

5. What is the complement of a 4 degree angle? .

6. What is the complement of 30º? .

7. What is the complement of xº? .

Solve for x by SETTING UP AN EQUATION:

8. 9.

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10. 11. Find both missing angles

.

12. 1:m 2 = 2:7. 13. m<1 : m<2 = 8 : 1

Find the measure of both angles. Find the measure of <1.

14. m<1 : m:2 = 2 : 3 15. m<1 = 2x + 40, m<2 = 4x - 10

Find the measure of both angles. Find the measure of <2

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Lesson 1 Homework

Complementary Angles

1. m 1 = 35º. Find m 2. 2. m 1 = 2x + 5 and m 2 = 3x + 15.

Find m 2.

3. m BID = 2x + 40 and m DIR = 4x – 10 4. m 1:m 2 = 5:4. Find the measure

Find the measure of both angles. of both angles.

5. AF AC . If m FAT = m CAT, **6. Given OE OU , m EOS = 10º and

find the measure of both angles. m MOU = 120º. Find m SOU

and m MOE.

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Lesson 2 Classwork

Supplementary Angles

Straight angle -

Supplementary angles -

** Using the above definition, the word sum tells us that we are using addition to set up an equation. The

word is tells us that the total is 180 degrees. **

Supplementary angles do not have to be adjacent to each other for them to be supplementary.

Notice in the diagram below to the left, when supplementary angles are adjacent to each other, they form a

straight angle. Below to the right, they are still supplementary, just not adjacent to each other. What this

means is: <1 + <2 = 180

1. Supplementary Angles are two angles whose sum is .

2. Supplementary angles form what type of angle? .

3. What is the supplement of a 40 degree angle? .

4. What is the supplement of a 4 degree angle? .

5. What is the supplement of 30º? .

6. What is the supplement of xº? .

Solve for x by SETTING UP AN EQUATION:

Find the missing angles. (<1 + <2 = 180)

2. 1.

x 82

7x 2x

6

4x 5x 3. 4.

5. m<1 = x + 30, m<2 = 4x + 40 6. m<1 = 3x + 15, m<2 = 2x + 5

Find m<1 Find m<2

7. m<1 : m<2 = 2 : 3 8. m<1 : m<2 = 7 : 3

9. A. Find the measure of x. B. Find the measure of y

15x + 60 5x

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Lesson 2 Homework

Supplementary Angles

1. m 1 = 135º. Find m 2. 2. m KIS = 2x + 10 and m SID = 4x + 20.

Find m DIS.

3. m TIS = 3x + 65 and m EIS = 2x – 35 4. m 1:m 2 = 7:3. Find the measure

Find the measure of both angles. of both angles.

*5. Use the picture below to determine the **6. Given line MOU and m EOS = 40º,

measure of each angle. Fill in all missing angles!

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Lesson 3 Classwork

Vertical Angles

Vertical angles

Their values are

=

=

Use the picture below for # 1 – 4 .

1. Name an angle congruent to angle 1.

2. Name an angle supplementary to angle 1.

3. If angle 1 = 70°, then : 2= , 3= , 4=

4. If angle 2 = 135°, then: 1= , 3= , 4=

Practice

1. Find all of the missing angles 2. Find all of the missing angles

x y z x y z

y

x 42

z

y

x 150

z

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3. Find all of the angles 4. Find all of the angles

y z y z

5. m 4 = 5x and m 2 = 3x + 20 6. m 1 = 3x – 10 and m 2 = 2x + 50

7. m 1 = x + 20 and m 2 = 2x + 40 8. Find each angle. Show all Work

y

x + 20 2x - 40

z

x + 20

2x + 40 y

z

1 = 30°

2 =

3 =

4 = 45°

5 =

6 =

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Lesson 3 Homework

Vertical Angles

1. m 1 = 35º. Find m 2, m 3 2. If m 1 = x + 15 and m 3 = 2x, find m<2

and m 4.

3. If m 2 = 7x + 18 and m 4 = 5x + 48, 4. If m 3 = 5x – 10 and m 4 = 45º. Find the

find m 2. measure of both angles.

*5. If m 2 = 42º and m 4 = 92º, find m 6. *6. Given lines CN and UK, SH SN and

m USN = 50º. Find m 1, m 2,

m 4, and m 5.

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1 2

Lesson 4 Classwork

Mixed Review of Angles

1. Find the measure of ‹ 2

m‹ 1 = 15x, m ‹ 2 = 5x

2. m ‹ 1: m ‹ 2 = 4:5 . Find the measure of ‹ 1.

1

3. Solve for x in the diagram below.

4. Us the diagram below to answer the questions: If m ‹ 1 = 89, find ….

m‹ 2:

m‹ 3:

m‹ 4:

5. What is the supplement of a) 145 b) 89 c) x d) 35

6. What is the complement of: a) 3x b) 83 c) x d) 1

1 2

x + 12

4x + 8

1

2 3

4

12

1

2

4 3

1 2

7. AB BC Find the measure of <ABD: B C

2x + 40

x – 10

D

A

8. Find the measure of all four angles.

m ‹ 1 = 2x – 50

m ‹ 2 = x + 10

9. If the m‹ 1: m‹2 = 8:1, fin the m‹ 1.

10. m ‹ 5 = 2x + 5

m ‹7= 4x-35

Solve for x.

11. HS is perpendicular to SN. If m<2 = 40, find all other angles.

5 6

8 7

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Use the diagram to answer the questions.

1. Lines a and b are

2. Line c is called the

3. Name a pair of vertical angles: & _

4. Name a pair of corresponding angles: &

Lesson 5 Classwork

Parallel Lines – Numerical

Angle Relationship Formed Examples

Supplementary Angles

Vertical Angles

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

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5. Name a pair of alternate interior angles: &

6. Name a pair of alternate exterior angles: &

7. Name a pair of supplementary angles: &

8. Name a pair of congruent angles: &

9. True or False: 1 5? 10. True or False: 1 6?

11. True or False: 4 5? 12. True or False: 4 6?

13. If m 1 = 60º, then: 14. If m 6 = 100º, then:

m 2 = m 1 =

m 3 = m 2 =

m 4 = m 3 =

m 5 = m 4 =

m 6 = m 5 =

m 7 = m 7 =

m 8 = m 8 =

15

1 3

2

4 a

5 6 7 8

c

Use this diagram to answer the following questions

Lesson 5 Homework

Parallel Lines – Numerical

b

Tell what type of angle each pair is:

(supplementary, vertical, corresponding, alternate interior, alternate exterior angles)

1. <1 and < 5 4. <5 and <8

2. <2 and <7 5. <3 and <6

3. <5 and <6 6. <1 and <4

7. Give the measure of each angle if m<2 = 750

<1 = <3 = <4 = _ <5= <6 = <7= <8 =

8. Give the measure of each angle if m <5 = 1080

<1 = <2 = <3 = _ <4= <6 = <7= <8 =

9. Give the measure of each angle if m<8 = 1000

<1 = <2 = <3 = _ <4= <5 = <6= <7 =

10. True or False: Angles 3 and 5 are congruent.

11. True or False: Angles 3 and 6 are congruent.

12. Name the parallel lines:

13. Name the transversal:

For each of the following, find the missing angle AND state the angle relationship

14. If m<5 = 950, fine m<8 16. If m<8 = 117

0, find m<4

15. If m<1 = 1200, find m<8 17. If m<6 = 32

0, find m<3

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Lesson 6 Classwork

Parallel Lines – Algebraic

1. m1 37, m8 ? 2. m3 40, m5 ?

3. m4 5x 10, m5 3x 40, m5 ? 4. m8 3x 30, m3 x 80, m8 ?

5. m3 4

m5. Find m5. 5

6. m6 : m2 3 : 7. Find m6.

7. m4 5x 12, m2 2x 51. Find m8.

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1. If m 3 = 3x – 10 and m 6 = x + 80, find x.

2. If m 2 = 5x and m 6 = x + 20, find m 2.

3. If m 3 = 3x – 10 and m 5 = 2x + 40, find m 5.

Lesson 6 Homework

Parallel Lines – Algebraic

4. If m 6 = 4x + 20 and m 1 = 3x + 90, find the measure of all eight angles.

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Lesson 7 Classwork

Understanding Triangles

The sum of the angles of ANY triangle is .

Types of angles.

1. Base Angle:

2. Vertex Angle:

3. Interior:

4. Exterior:

Types of triangles:

1. Acute:

2. Obtuse:

3. Right:

4. Equilateral:

5. Isosceles:

1. Find the measure of the vertex angle of an isosceles if a base angle measures 55º.

2. The measures of the angles of a triangle are represented by 2x, 3x, and x. Find the measure of each

angle.

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3. The measure of each base angle of an isosceles is half the base angle. Find the measure of each angle

of the triangle.

4. Given the triangle below:

a) If m 1 = 30º and m 2 = 90º, find m 3 and m 4.

b) What type of triangle is it?

5. a) Find the value of x:

b) What type of triangle is it?

6. The measure of an exterior angle to a base angle of an isosceles triangle is 115º. What is the measure

of the vertex angle of the triangle?

7. The measures of the angles of a triangle are in the ratio 2:4:9. Find the measures of the angles.

8. Find the value of x:

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Lesson 7 Homework

Understanding Triangles

1. Find the measure of a base angle of an isosceles if the vertex angle measures 55º.

2. In ABC, m A = x, m B = x + 30, and m C = 2x - 10. Find the measures of each angle and

determine what type if triangle it is.

3. Solve for x. 4. Find the measure of each angle.

5. Solve for x.

6. Solve for x.

7. If m 3 = 90º and m 5 = 147º, find the measure

of the other angles.

8. Angle 1 = 45º and angle 2 = 70º. Find the

measure of the exterior angle at 4.

If m<1 = 30 and m<8 = 120, find ALL other

angles.

m<2 = m<11 = m<20 = m<3

= m<12 = m<21 = m<4 =

m<13 = m<22 = m<5 = m<14

= m<23 = m<6 = m<15 =

m<7 = m<16 =

m<17 = m<9

= m<18 = m<10 =

m<19 =

Lesson 8 Classwork

Triangles and Parallel Lines

1. If m 1 = 60º and m 3 = 50º, then:

m 1 = m

2 = m

3 = m 4

= m 5 =

m 6 =

m 8 = m

9 = m

10 =

m 11 = m

12= m 13

=

m 7 = m 14 =

2)

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3)

1 2

5

3 4 6

7 11 12

8 9 10 13 14

If m<6 = 60 and m<8 = 40, find ALL other

angles.

m<1 = m<10 = m<2

= m<11 = m<3 =

m<12 = m<4 = m<13

= m<5 = m<14 =

m<7 =

m<9 =

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Lesson 8 Homework

Triangles and Parallel Lines

1. If m 1 = 70º and m 6 = 80º, then:

m 1 = m

2 = m

3 = m 4

= m 5 =

m 6 = m

7 = m

8 =

m 11 = m

12 = m

13 =

m 14 =

m 15 =

m 16 = m

17 = m

18 =

m 9 = m 19 =

m 10 =

Given that the vertical lines are parallel:

find the values of a, b, and c (in that order).

find the measures of the 4 labeled angels.