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The Jungle

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Answer Key

Name ________________________
Common Core Geometry R

Date __________________
HW # 1 (Finding missing angles)
A

1. Use the following diagram to answer the questions below:
J

F
H

Z
G

a. Name an angle supplementary to

conclusion.
≮HZG or ≮JZF

HZJ and provide the reason for your

Linear pairs form supplementary angles.

b. Name an angle complementary to

HZJ and provide the reason for your

conclusion.
≮JZA

The supplement of a 900 angle measure 900.

c. If m HZJ = 38, what is the measure of each of the following angles? Provide

reasons for your calculation.
(1)

380

Vertical angles are equal in measure.

(2)

1420

(3)

520

Linear pairs form supplementary angles.

Complementary angles are two angles that sum to 900.

#2-6 Find the values of x and/or y. Show all steps to your solution, and give reasons for your calculations.
2.

c

B
112
y0

680

A

0

(4x ­ 2)0
300

68 + y = 180 y = 1120 Linear pairs form suppl. ≮s.

4x - 2 + 142 = 180
Consecutive adjacent angles on a x = 10 line sum to 1800.
D

OVER

3.

4.

C

D
A

x0

x0

y0

B

470

240

A

C

B

x0

47 + y = 90 y = 43
Complementary angles sum to 900.

2x + 24 = 180 x = 78
Consecutive adjacent angles on a line sum to 1800.

D

47 + x = 180 x = 133
Linear pairs form supplementary angles.

5.
6.

D

A

A

(2x + 1)0

y0

C

(5x + 45)0

(2x ­ 5)0
(3x ­ 25)0

D

E

(3x + 10)0

(y ­ 3)

y0

91

8x + 20 = 180 x = 20
Linear pairs form supplementary angles. y + 5x - 30 = 180 y + 70 = 180 y = 110
Consecutive adjacent angles on a line sum to 1800.

F

0

550

0

C
5 8/9 x + 21 = 180
53/9 x = 159 x = 27
Consecutive adjacent angles on a line sum to 1800. y - 3 + y = 91 y = 47
**Angle addition postulate**

340

B

Aim 2: How do identify angles formed by parallel lines and a transversal, and find angle measures?

Corresonding Angles (4 pairs)

Corresponding
Corresponding

Corresponding

Corresponding

Corresponding

Corresponding

Corresponding Corresponding

Aim 2: How do identify angles formed by parallel lines and a transversal, and find angle measures?

Same Side Interior Angles (2 pairs)

Same Side Interior <

Same side interior <

Same Side Interior <

Same side interior <

Aim 2: How do identify angles formed by parallel lines and a transversal, and find angle measures?

Alternate Interior Angles (2 pairs)

Alternate Interior Alternate Interior

Alternate Interior

Alternate Interior

Corresponding Angles

1

2

Alternate Interior Angles

1
2

Same-Side Interior Angles

1
2
How would you "classify" angle 1 and angle 2?

KEY FACTS Aim 2

Aim 2

Aim 2

Aim 2

Aim 2

Aim #2: How do we solve for unknown angles formed by transversals?

Do Now: Use the diagram to determine x and y. AB and CD are line segments.
a) Solve for x and y.
E

D x + 8

b) Name a pair of vertical angles.
2x ­ 8

A

O

B

y

c) Find m≮BOF. Justify your calculation.

4x ­ 24

F

C

Name the four pairs of corresponding angles.

E
A

a b c d

e f g h

C

B

Name the two pairs of alternate interior angles.
D

Name the two pairs of same side interior angles.

F

transversal
If a transversal intersects two parallel lines, then corresponding angles are equal in measure. "F"

If a transversal intersects two parallel lines, then alternate interior angles are equal in

measure.

"Z"
If a transversal intersects two parallel lines, then same-side interior angles are supplementary. "C"
Examples: Find the measure of the angle marked with a variable.
a.

c.

b.
480

d.

480

480
480

e. An auxiliary line is sometimes useful when solving for unknown angles. Explain how the auxiliary line (dashed) is used to find m≮e and m≮f.

What is m≮W? ______

Exercises: Find the unknown (labeled) angles.
Choose the reason (A-F) that justifies your solution.
A: If parallel lines are cut by a transversal, alternate interior angles are =.
B: If parallel lines are cut by a transversal, same-side interior angles are supplementary.
C: If parallel ines are cut by a transversal, corresponding angles are =.
D: Adjacent angles on one side of a line sum to 1800.
E: The sum of the angles of a triangle is 1800.
F: Vertical angles are =.

1.

2.

3. (First draw an auxiliary line.)

4.
1040
A

x = ______
2x­10
C

B

m≮ABC = ______

A: If parallel lines are cut by a transversal, alternate interior angles are =.
B: If parallel lines are cut by a transversal, same-side interior angles are supplementary.
C: If parallel ines are cut by a transversal, corresponding angles are =.
D: Adjacent angles on one side of a line sum to 1800.
E: The sum of the angles of a triangle is 1800.
F: Vertical angles are =.

_____

5.

_____

_____
≮n = ____________________

6.

_____

_____ n _____

7. You will need to draw two auxiliary lines to find a.
Write out the reason that justifies your solution.

8. Solve for x, y, and z.

x­10 y z

4x­130

Let's sum it up!!!
If parallel lines are cut by a transversal,
• alternate interior angles are equal in measure.
• corresponding angles are equal in measure.
• same side interior angles are supplementary.
• An auxiliary line may be drawn into a diagram to create one of the above pairs of angles cut by a transversal, so that unknown angles can be determined.

7.

8.

x­10 y 4x­130

z

Name____________________
CC Geometry R

Date_____________
HW #2 (Missing angles and transversals)

Find the unknown (labeled) angles. Write out reasons for your solutions.
1.

2.

3. Draw an auxiliary line.

4. Draw an auxiliary line.

5. Draw an auxiliary line.

OVER

6. b 360

≮b = _____

7.
1400

a
660

b

8.

9.

≮a = _____
≮b = _____

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