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The image shows two intersecting lines forming an angle labeled "y," with expressions \( (3x + 20)^\circ \) and \( (5x - 50)^\circ \) representing the angles on either side of the intersection. Since these are vertically opposite angles, they are equal.

We can set up the following equation:

\[
3x + 20 = 5x - 50
\]

Now let's solve for \( x \):

\[
3x + 20 = 5x - 50
\]
\[
20 + 50 = 5x - 3x
\]
\[
70 = 2x
\]
\[
x = 35
\]

Now that we know \( x = 35 \), we can substitute it back into either of the angle expressions to find the value of \( y \). Let’s use the first expression \( 3x + 20 \):

\[
y = 3(35) + 20 = 105 + 20 = 125^\circ
\]

So, the value of \( y \) is \( 125^\circ \).

Would you like more details or have any questions about this solution?

Here are five related questions you might find useful:
1. What are vertically opposite angles, and why are they always equal?
2. Can you solve the equation if different angles were given for the expressions?
3. How can you determine if two angles are supplementary or complementary?
4. What are alternate interior angles, and how are they used in geometry?
5. How would this problem change if the two lines were parallel?

**Tip:** Vertically opposite angles are always equal because they are formed by two intersecting lines, and the pairs of angles directly across from each other are congruent.

Given two intersecting lines forming an angle, where one angle is represented as (3x + 20)° and the opposite angle is represented as (5x - 50)°, find the value of y.

Learn how to solve a vertically opposite angles problem using algebra, with angles represented as (3x + 20)° and (5x - 50)°. Suitable for students in Grades 8-10.

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