You can use the properties of vertical angles to solve the algebraic expressions of two vertical angles. Two lines that intersect one another create four angles, or two pairs of vertical angles. Vertical angles are the angles that are nonadjacent and opposite each other. They share the same vertex, which is the corner or point where the two lines meet, and are congruent, or equal to each other. For example, if one vertical angle is 45 degrees, the other vertical angle is also 45 degrees. Therefore, an algebraic expression of one vertical angle is equal to an algebraic expression of the other vertical angle.

Determine the expressions of two vertical angles. For the following example, use 3x + 30 as the expression of one vertical angle and 2x + 60 as the expression of the other vertical angle.

Set the expressions equal to each other. In the example, this results in the equation 3x + 30 = 2x + 60.

Subtract the term with the variable on the right side of the equation from both sides of the equation to isolate the terms that contain the variable on the left side of the equation. In the example, subtract 2x from both sides of the equation, which results in 3x + 30  2x = 2x + 60  2x. This leaves x + 30 = 60.

Subtract any remaining terms on the left side of the equation from both sides of the equation to isolate and solve for the variable. In the example, subtract 30 from both sides of the equation, which results in x + 30  30 = 60  30. This leaves x = 30, which is the solution to the expressions for both vertical angles.

Substitute the solution for the variable in either one of the original vertical angle expressions. In the example, substitute 30 for x in the expression 3x + 30, which equals 3(30) + 30.

Solve the expression to determine the measure of each vertical angle. In the example, solve 3(30) + 30, which simplifies to 90 + 30, which equals 120. This is the measure of each vertical angle.
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