Answer:
6a. x = 5/3
6b. x = 2
7a. x = 17
7b. y = 30, x = 3
8. 90-55 = 35
9. 180-30=150
10. 17 - 5 =12
11. opposite and corresponding angles (explanation beneath)
Step-by-step explanation:
6a. 7x-10=x+2
7x=x+10 (add 10 to both sides)
6x=10 (subtract x from both sides)
x = 5/3
6b. -3x+5(3x-1)=2x+15
12x-5=2x+15 (simplify the left side)
12x=2x+20 (add 5 to both sides)
10x=20 (subtract 2x from both sides)
x = 2
7a. (3x-10)+(2x+15) = 90
90+10= 100
100-15= 85
85/5 = 17 (as 3x + 2x = 5x)
x = 17
7b. 5y-45 = 3y +15
5y = 3y +60 (add 45 to both sides)
2y = 60 (subtract 3y from both sides)
y = 30
sub 30 for y into 3y+15: 90+15=105
straight line = 180
180-105=75
25x=75
75/25=3
x=3
8. complementary means 90º total
90-55=35 or 55+35 = 90
9. linear pair mean 180º total
180-30=150 or 30+150 =180
10. LF = 17
as LE is equal to FT, they both are equal to 5
as LE is part of LF, 17 - 5 =12
11. lm and rs are parallel
given that 9 and 12 are opposite angles, and that 12 and 8 are corresponding angles, meaning that 12 and 8 are of the same angle.
and since 12 = 8, and 12 = 9,
therefore you can prove that 8 = 9
