Answer:
The value of x and y are x = 15 and y = 63
Step-by-step explanation:
From the given figure
∵ The angles of measures (9x - 7)° and (4x - 8)° are adjacent angles
∵ The angles of measures (9x - 7)° and (4x - 8)° formed a line
∴ They formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
→ That means add them and equate the sum by 180
∴ (9x - 7) + (4x - 8) = 180
→ Add the like terms
∵ (9x + 4x) + (-7 + -8) = 180
∴ 13x + (-15) = 180
→ Remember (+)(-) = (-)
∴ 13x - 15 = 180
→ Add 15 to both sides
∴ 13x - 15 + 15 = 180 + 15
∴ 13x = 195
→ Divide both sides by 13
∵ [tex]\frac{13x}{13}[/tex] = [tex]\frac{195}{13}[/tex]
∴ x = 15
∵ Lines m and n are parallels
∵ A line intersected them
∵ The angles of measures (2y + 2), (9x - 7) are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ 2y + 2 = 9x - 7
∵ x = 15
→ Substitute the value of x
∴ 2y + 2 = 9(15) - 7
∴ 2y + 2 = 135 - 7
∴ 2y + 2 = 128
→ Subtract 2 from both sides
∴ 2y + 2 - 2 = 128 - 2
∴ 2y = 126
→ Divide both sides by 2
∴ [tex]\frac{2y}{2}[/tex] = [tex]\frac{126}{2}[/tex]
∴ y = 63
The values of x and y are 15 and 63, respectively
The angles in the figure are: (9x - 7)° and (4x - 8)°
These angles are adjacent angles.
So, we have:
[tex]\mathbf{9x - 7 + 4x - 8 = 180}[/tex]
Collect like terms
[tex]\mathbf{9x + 4x = 180 + 8 + 7}[/tex]
[tex]\mathbf{13x = 195}[/tex]
Divide both sides by 13
[tex]\mathbf{x = \frac{195}{13}}[/tex]
[tex]\mathbf{x = 15}[/tex]
Also, we have:
[tex]\mathbf{2y + 2 = 9x - 7}[/tex] -- interior angles
Subtract 2 from both sides
[tex]\mathbf{2y = 9x - 9}[/tex]
Substitute 15 for x
[tex]\mathbf{2y = 9\times 15 - 9}[/tex]
[tex]\mathbf{2y = 126}[/tex]
Divide both sides by 2
[tex]\mathbf{y = 63}[/tex]
Hence, the values of x and y are 15 and 63, respectively
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