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find the values x and y given : m is parallel to n, angle 4= 6x-5, angle 10 = 5x + 8, angle 9 = 3y - 10

User Haptn
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Answer:

Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.

First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:

angle 4 = angle 9 (alternate interior angles)

angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)

angle 4 + angle 10 = 180 degrees (corresponding angles)

Substituting the given expressions for each angle, we have:

6x - 5 = 3y - 10

5x + 8 + 3y - 10 = 180

6x - 5 + 5x + 8 = 180

Simplifying the second equation by combining like terms, we get:

8x + 3y - 2 = 0

We can now solve for one variable in terms of the other. From the first equation, we have:

6x = 3y + 5

x = (3/2)y + (5/6)

Substituting this expression for x into the third equation, we get:

6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180

Simplifying and solving for y, we get:

y = 29/9

Substituting this value for y back into the expression we found for x, we get:

x = (3/2)(29/9) + (5/6) = 59/6

Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.

User Tom Scogland
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