120° (2x + 10)° (2y + 30)° Using the angle relationships, determine the value of y in the diagram above y = 15 y = 30. y = 45 y = 90

1 answer

To find the value of y in the given diagram, we need to use the angle relationships.

We are given that the angle 120° is equal to (2x + 10)° (2y + 30)°.
So, we can set up the equation as follows:

120 = (2x + 10)(2y + 30)

Expanding the equation, we get:

120 = 4xy + 60x + 20y + 300

Rearranging the terms, we get:

4xy + 60x + 20y + 180 = 0

To solve for y, we need to rewrite the equation in terms of y:

4xy + 20y = -60x - 180

Factoring out y from the left side of the equation, we get:

y(4x + 20) = -60x - 180

Dividing both sides by (4x + 20), we get:

y = (-60x - 180) / (4x + 20)

Simplifying the right side of the equation, we get:

y = -15(x + 5) / (x + 5)

The term (x + 5) cancels out, giving us:

y = -15

Thus, the value of y is -15.