Direction: Find the values of x and y in the following figures. 1. (21y - 1)°, (4x + 23)°, (9x - 38)° 2....

Question

Direction: Find the values of x and y in the following figures.
1. (21y - 1)°, (4x + 23)°, (9x - 38)°
2. 5y°, (15x + 10)°, 85°
3. (4x + 6)°, 74°, 2y°
4. (9x + 42)°, 15x°, (4y - 13)°
5. (2y - 50)°, 80°, (3x - 1)°
6. (9x + 12)°, 3x°, (4y - 10)°

SnapAndSolve AI · Accepted Answer

Using the property of vertically opposite angles:
(21y - 1)° = (9x - 38)°
21y - 1 = 9x - 38
21y = 9x - 37
Also, (4x + 23)° = (9x - 38)°
4x + 23 = 9x - 38
5x = 61
x = 12.2
Substitute x = 12.2 into 21y = 9x - 37:
21y = 9(12.2) - 37
21y = 72.8
y = 3.47
Using the property of supplementary angles:
5y + 85 = 180
5y = 95
y = 19
Also, (15x + 10)° = 85°
15x + 10 = 85
15x = 75
x = 5
Using the property of supplementary angles:
(4x + 6) + 74 = 180
4x + 80 = 180
4x = 100
x = 25
Also, 2y = 74
y = 37
Using the property of vertically opposite angles:
(9x + 42)° = (4y - 13)°
9x + 42 = 4y - 13
4y = 9x + 55
Also, (9x + 42)° = 15x°
9x + 42 = 15x
6x = 42
x = 7
Substitute x = 7 into 4y = 9x + 55:
4y = 9(7) + 55
4y = 118
y = 29.5
Using the property of supplementary angles:
(2y - 50) + 80 = 180
2y + 30 = 180
2y = 150
y = 75
Also, (3x - 1)° = 80°
3x - 1 = 80
3x = 81
x = 27
Using the property of vertically opposite angles:
(9x + 12)° = (4y - 10)°
9x + 12 = 4y - 10
4y = 9x + 22
Also, (9x + 12)° = 3x°
9x + 12 = 3x
6x = -12
x = -2
Substitute x = -2 into 4y = 9x + 22:
4y = 9(-2) + 22
4y = 4
y = 1

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Direction: Find the values of x and y in the following figures. 1. (21y - 1)°, (4x + 23)°, (9x - 38)° 2....

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