All answers are down below!
Step-by-step explanation:
PAGE 1
22.) -10x - 2y = 20 (add 10x on both sides)
-2y = 10x + 20 (divide by -2 on both sides)
y = -5x - 10
Neither because perpendicular lines have opposite reciprocal and opposite sign. This equation only has opposite sign. It's not parallel because parallel lines have the same slope, and this equation doesn't.
23.) <1 = 138 b/c 180 -42
<2 = 42 b/c vertical to the angle measured 42
<3 = 138 b/c it's vertical to <1 and vertical angles have the same measure
<4 = 42 b/c it is an alternate interior angle to <2
<5 = 90 b/c vertical to <8
<6 = 48 b/c <4 + <5 + <6 = 180 and 42 + 90 + 48 = 180
<7 = 42 b/c it is vertical to <4 which also has a measure of 42
<8 = 90 b/c it is same side interior to <10 which has a measure of 90 degrees
<9 = 48 b/c <7 + <8 = 132 and 180 -132 = 48
<10 = 90 b/c it is a linear pair with the right angle and a right angle equals 90 degrees
PAGE 2
1.) PQ, QR, and NR
2.) ML, NP, and RQ
3.) KL, JM, JN, and KP
4.) corresponding angles
5.) alternate interior angles
6.) alternate exterior angles
7.) interior consecutive angles or same side interior angles
PAGE 3
9.) Q'(5, -4) R'(5, -2) S'(1, -3) because (x, y) > (-x, y)
10.) J'(3, 5) I'(1, 1) H'(3, 1) G'(4, 5) b/c (x,y) > (x, -y)
11.) E'(1, -4) F'(0, -2) G'(-3, -5) b/c (x,y) > (-x, y)
12.) J'(1, 2) K'(-1, -3) L'(4, -2) M'(3, 3) b/c (x,y) > (x, -y)
13.) Y'(-4, 1) X'(-3, 4) W'(-4, 5) b/c (x,y) > (y, x)
14.) J'(-3, 3) I'(5, 2) H'(-5, 1) G'(0, -1) b/c (x,y) > (-y, -x)
15.) H'(-2, 5) G'(2, 2) F'(3, 4) b/c (x,y) > (x, -y)
16.) U'(-2, -1) V'(0, 2) W'(-3, 4) b/c (x,y) > (y, x)
PAGE 4
17.) 3x - 43 = 80 (add 43 on both sides) --> 3x = 123 (divide by 3 on both sides) --> x = 41
18.) 8x - 6 = 90 (add 6 on both sides) ---> 8x = 96 (divide by 8 on both sides) --> x = 12
19.) 15x - 5 + 11x + 3 = 180 (collect like terms) --> 26x -2 = 180 (add 2 on both sides) ---> 26x = 182 (divide by 26 on both sides) --> x = 7
20.) To find slope use y2-y1/x2-x1
PLUG IN
2 - -5/ -1 - -5 =
7/4 since parallel lines have the same slope line b would also have a slope of 7/4.
21.) x + 3y = 2 (subtract x on both sides) ---> 3y = -x + 2 (divide by 3 on both sides)
y = -1/3x + 2/3. The lines are perpendicular because their slopes have opposite reciprocals and opposite signs.
PAGE 5
8.) 4x - 9 + 75 = 180 (collect like terms) --> 4x + 66 = 180 (subtract 66 on both sides) > 4x = 114 (divide by 4 on both sides) x = 28.5
9.) 7x + 2 = 65 (subtract 2 on both sides) --> 7x = 63 (divide by 7 on both sides) --> x =9
10.) Corresponding angles
11.) <7
12.) consecutive interior angles or same side interior angles
13.) <9
14.) Line C
15.) c || d
16.) a || b
Hope this helps you!!
