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3-2


4. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy’s wake as a line. m∠1 = (2x + 2y)° and m∠2 = (2x + y)°. Find x and y. x = _________ y = _________

Name________________________________________ Date__________________ Class__________________

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3-2


Use the diagram of a staircase railing. AG ||CJ and AD || FJ . Choose the best answer.

5. _____ Which is a true statement about the measure of ∠DCJ? A It equals 30°, by the Alternate Interior Angles Theorem. B It equals 30°, by the Corresponding Angles Postulate. C It equals 50°, by the Alternate Interior Angles Theorem. D It equals 50°, by the Corresponding Angles Postulate.

6. _____ Which is a true statement about the value of n? F It equals 25°, by the Alternate Interior Angles Theorem. G It equals 25°, by the Same-Side Interior Angles Theorem. H It equals 35°, by the Alternate Interior Angles Theorem. J It equals 35°, by the Same-Side Interior Angles Theorem.

7. In the diagram, which represents the side view of a mystery spot,

mSRT = 25°, RT

is a transversal to

PS &QR .

a) What type of angle pair is QRT & STR?

b) Find mSTR. Use a postulate or theorem to justify your answer

Name________________________________________ Date__________________ Class__________________

30. Land Development A piece of property

2

1lies between two parallel streets as shown. m!1 = (2x + 6) °, and m!2 = (3x + 9) °. What is the relationship between the angles? What are their measures?

31. /////ERROR ANALYSIS///// In the figure, AD

BC

m!ABC = (15x + 5) °, and m!BCD = (10x + 25) °. Which value of m!BCD is incorrect? Explain.

A B

m!BCD = 10(4) + 25 = 65˚

- -

+ =- -

+ = +

=

=

+ + + =

m!BCD = 10(6) + 25 = 85˚

=

=

+ =

- -

32. Critical Thinking In the diagram, ! " m.

m

x˚

x˚

y˚!Explain why x _ y = 1.

33. Write About It Suppose that lines ! and m are intersected by transversal p. One of the angles formed by ! and p is congruent to every angle formed by m and p. Draw a diagram showing lines !, m, and p, mark any congruent angles that are formed, and explain what you know is true.

34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R

V T U

S Find m!RVT.

15° 65° 27.5° 77.5°

29. In the diagram, which represents the side view of P

S

Q

RT

a mystery spot, m!SRT = 25°. # $% RT is a transversal

to # $% PS and # $% QR .

a. What type of angle pair is !QRT and !STR?

b. Find m!STR. Use a theorem or postulate to justify your answer.

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160 Chapter 3 Parallel and Perpendicular Lines

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LESSON

x-x

3-173-17

LESSON

3-2

CS10_G_MECR710617_C03L02f.indd 17 4/8/11 9:56:41 AM

8.


2



BC


A B

m!BCD = 10(4) + 25 = 65˚

- -

+ =- -

+ = +

=

=

+ + + =

m!BCD = 10(6) + 25 = 85˚

=

=

+ =

- -


m

x˚

x˚



34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R

V T U

S Find m!RVT.

15° 65° 27.5° 77.5°


S

Q

RT


to # $% PS and # $% QR .



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9. In the diagram, || m,Explain why xy= 1.

10. Suppose that lines ℓ and m are intersected by transversal p. One of the angles formed by ℓ and p is congruent to every angle formed by m and p. Draw a diagram showing lines ℓ, m, and p, mark any congruent angles that are formed, and explain what you know is true.


2



BC


A B

m!BCD = 10(4) + 25 = 65˚

- -

+ =- -

+ = +

=

=

+ + + =

m!BCD = 10(6) + 25 = 85˚

=

=

+ =

- -


m

x˚

x˚



34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R

V T U

S Find m!RVT.

15° 65° 27.5° 77.5°


S

Q

RT


to # $% PS and # $% QR .



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Name________________________________________ Date__________________ Class__________________


2



BC


A B

m!BCD = 10(4) + 25 = 65˚

- -

+ =- -

+ = +

=

=

+ + + =

m!BCD = 10(6) + 25 = 85˚

=

=

+ =

- -


m

x˚

x˚



34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R

V T U

S Find m!RVT.

15° 65° 27.5° 77.5°


S

Q

RT


to # $% PS and # $% QR .



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2



BC


A B

m!BCD = 10(4) + 25 = 65˚

- -

+ =- -

+ = +

=

=

+ + + =

m!BCD = 10(6) + 25 = 85˚

=

=

+ =

- -


m

x˚

x˚



34. m!RST = (x + 50) °, and m!STU = (3x + 20) °. R

V T U

S Find m!RVT.

15° 65° 27.5° 77.5°


S

Q

RT


to # $% PS and # $% QR .



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Find m∠1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.) 11. 12.

35. For two parallel lines and a transversal, m!1 = 83°. For which pair of angle measures is the sum the least?

!1 and a corresponding angle !1 and a same-side interior angle !1 and its supplement !1 and its complement

36. Short Response Given a " b with transversal t,

a b

t

1 2

3explain why !1 and !3 are supplementary.

CHALLENGE AND EXTENDMulti-Step Find m!1 in each diagram. (Hint: Draw a line parallel to the given parallel lines.)

37.

1

145˚

40˚

38. 1

105˚

80˚

39. Find x and y in the diagram. Justify your answer.

40. Two lines are parallel. The measures

m

n

pq

72˚

(10x + 5y)˚

(15x + 4y)˚80˚

of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.

3-2 Angles Formed by Parallel Lines and Transversals 161





a b

t

1 2



37.

1

145˚

40˚

38. 1

105˚

80˚



m

n

pq

72˚

(10x + 5y)˚

(15x + 4y)˚80˚





14. Two lines are parallel. The measures of two corresponding angles are a° and 2b°, and the measures of two same-side interior angles are a° and b°. Find the value of a.

Name________________________________________ Date__________________ Class__________________




a b

t

1 2



37.

1

145˚

40˚

38. 1

105˚

80˚



m

n

pq

72˚

(10x + 5y)˚

(15x + 4y)˚80˚




0*0$$%$’12%&’0,’3*0&4%*&0$&’ lesson !#$%&$’()( · 8. 30. land...

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00$$%$’12%&’0,’30&4%*&0$&’ lesson !#$%&$’()( · 8. 30. land...