Answer: 14. x = 16; y = 23
15. x = 9; y = 13
Step-by-step explanation:
14. (4x + 4) = (7x - 44) (alternate exterior angles are congruent)
4x + 4 = 7x - 44
Collect like terms
4x - 7x = -4 - 44
-3x = -48
Divide both sides by -3
x = -48/-3
x = 16
39° + (8y - 43)° = 180° (consecutive exterior angles are supplementary)
39 + 8y - 43 = 180
Add like terms
-4 + 8y = 180
Add 4 to both sides
8y = 180 + 4
8y = 184
Divide both sides by 8
y = 184/8
y = 23
15. (15x - 26)° = (12x + 1)° (alternate exterior angles are congruent)
15x - 26 = 12x + 1
Collect like terms
15x - 12x = 26 + 1
3x = 27
Divide both sides by 3
x = 27/3
x = 9
28° + (12x + 1)° + (4y - 9)° = 180° (sum of interior angles of ∆)
Plug in the value of x
28 + 12(9) + 1 + 4y - 9 = 180
28 + 108 + 1 + 4y - 9 = 180
Add like terms
128 + 4y = 180
Subtract 128 from each side of the equation
4y = 180 - 128
4y = 52
Divide both sides by 4
y = 52/4
y = 13
Both answer and explantion.
You can use the cosine law with the formula:
a^2 = b^2 + c^2 - 2*b*c*cosA
With a = 5, b = 5, c = 7,
7^2 = 5^2 + 5^2 - 2*5*7*cosA
49 = 25 + 25 - 70*cosA
70*cosA = 25 + 25 - 49
70*cosA = 1
cosA = 1/70
A = arccos (1/70) = 89.18 deg = 89 deg
If you are just adding those two decimals together, the answer would be 100.871.
83.971
+ 10.900 (make believe there are two zeros)
—————-
100.871
