Triangle NQP is an equilateral triangle with the measure of angle N=5x-2y and the measure of angle P=x+2y. Find the values of x and y.

Clue: isn't each angle of an equilateral angle equal to 60º ?

if NQP is an equilateral triangle measure of the angle N and P must be equal to 60.

5x-2y=60
x+2y=60
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6x=120
x=20 and also y=20

To find the values of x and y, we can set up a system of equations based on the given information.

Since Triangle NQP is an equilateral triangle, all of its angles must have the same measure. Therefore, we can set the measure of angle N equal to the measure of angle P:

5x - 2y = x + 2y.

Next, we can simplify this equation:

4x - 4y = 0.

Now, we have one equation with two variables. To solve for x and y, we would need another equation. However, the problem does not provide any additional equations or information.

Therefore, we cannot determine the exact values of x and y. We can only conclude that the variables x and y can take on any values as long as they satisfy the equation 4x - 4y = 0.

If there was another equation or piece of information relating to x and y, we could use it to solve for the variables. But in this case, there are multiple possible values for x and y that satisfy the given condition.