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1-4 HW Answers

12.

Q 21.

Right 13.

P 14.

R 15.

M 16.

TP & PQ 17.

VN & NM 18.

NR & NM 19.

PR & RQ 20.

<4 23.

<8 25.

<4 26.

P,T 27.

Q,S 28.

<9 & <3 29.

<9 & <2 31.

Right 32.

Acute 33.

Acute 34.

Obtuse 35.

Obtuse 36.

Answers will vary 37.

27 39. 16 41. 47

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1-5 Angle Relationships

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Real-Life

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Vocabulary

 Adjacent Angles- 2 angles that lie in the same plane and have a common vertex, but no common interior points  Linear Pair- a pair of adjacent angles with non-common sides that are opposite rays  Vertical Angles- 2 nonadjacent angles formed by 2 intersecting lines – VERTICAL ANGLES ARE CONGRUENT  Complementary angles- 2 angles with measures that have a sum of 90  Supplementary angles- 2 angles with measures that have a sum of 180  Perpendicular- lines, segments, or rays that form right angles

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1 2

ADJACENT

3

2 1

4

VERTICAL

<1=<2 , <3=<4 1 2

SUPPLEMENTARY

1 2

LINEAR PAIR

1 2

COMPLEMENTARY PERPENDICULAR

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

Examples

1. Name a linear pair

(x-36)+x=180 2x-36=180 2x=216 x=108 (x-36) = 108-36 = 72

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

PRACTICE

1. Name a linear pair whose vertex is B

(2x+21)+x=90 3x+21=90 3x=69 x=23 (2x+21) = 2(23)+21= 67 X=23

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Examples

 5. If m ∠ RTS = 8x + 18, find the value of x so that TR ⊥ TS.

8x+18 = 90 8x = 72 x = 9 CAN YOU ASSUME?

 6. ∠ WZU is a right angle YES Markings tell us so  7. ∠ VZU is adjacent to ∠ YZX.

NO Vertical angles, not adj.

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PRACTICE

 5. If m ∠ PTQ = 3y − 10 and m ∠ QTR = y, find the value of y so that ∠ PTR is a right angle.

3y-10 +y = 90 4y -10 = 90 4y = 100 y=25 CAN YOU ASSUME?

 6. ∠ NQO and ∠ OQP are complementary.

NO- No right angle markings  7. ∠ SRQ and ∠ QRP is a linear pair.

Yes, straight line

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HW 1-5 Answers

9. < BFC & < DFE 29.

X = 7 11.

< FDG & < GDE 13.

< CBF &

< GDE 17.

< BAD 19.

X = 65 21.

Y = 85 23.

Y =21 , X = 48 25.

< F = 63 , < E = 117 31.

< JNP = 92 35.

A = 8, b = 54 37.

True 39.

can’t determine 41.

False