Answer:
See below.
Step-by-step explanation:
1.
Corresponding angles of similar triangles are congruent.
m<C = m<C'
4x - 30 = x + 15
3x = 45
x = 15
m<C = 4x - 30 = 4(15) - 30 = 60 - 30 = 30
m<C' = m<C = 30
m<A = 2x + 35 = 2(15) + 35 = 30 + 35 = 65
2.
Method: SAS
BC = AD
6a + 20 = a + 60
5a = 40
a = 8
AB = 5a - 12 = 5(8) - 12 = 40 - 12 = 28
BC = 6a + 20 = 6(8) + 20 = 48 + 20 = 68
CD = AB = 28
AD = a + 60 = 8 + 60 = 68
3.
Method: SAS
2x + 3y = 34
4x - y = 40
Multiply the second equation by 3:
12x - 3y = 120
Add this new equation to the first original equation to eliminate y.
14x = 154
x = 11
Substitute 11 for x in the second original equation and solve for y.
4x - y = 40
4(11) - y = 40
44 - y = 40
-y = -4
y = 4
4.
Method: ASA
2d + 10 = 45 - 3d
5d = 35
d = 7
AC = 45 - 3d = 45 - 3(7) = 45 - 21 = 24
EC = 2d + 10 = 2(7) + 10 = 14 + 10 = 24
DE = d + 8 = 7 + 8 = 15
5.
2x - 59 = x + 31
x = 90
DO = x + 31 = 90 + 31 = 121
OG = 2x - 59 = 2(90) - 59 = 180 - 59 = 121
DG = x - 7 = 90 - 7 = 83
