angle 1 and angle 2 are vertical angles. if angle 1 = 17x+1 and angle 2 = 20x-14 find angle 2 

For vertical angles, the angles are always equal to each other.

Given:
- Angle 1 = \(17x + 1\)
- Angle 2 = \(20x - 14\)

Since the angles are vertical:
\[
\text{Angle 1} = \text{Angle 2}
\]
So, set the expressions equal to each other:
\[
17x + 1 = 20x - 14
\]

To solve for \(x\), first, subtract \(17x\) from both sides:
\[
1 = 3x - 14
\]

Next, add 14 to both sides:
\[
15 = 3x
\]

Now, divide both sides by 3:
\[
x = \frac{15}{3} = 5
\]

Now that we have the value of \(x\), we can find the measure of Angle 2.

**Angle 2:**
\[
20x - 14 = 20(5) - 14 = 100 - 14 = 86^\circ
\]

Thus, the measure of Angle 2 is \(86^\circ\).

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. What is the relationship between vertical angles and the concept of congruence?
2. If Angle 1 was \(22x + 4\) and Angle 2 was \(25x - 8\), how would you solve for \(x\)?
3. Can vertical angles ever be complementary? Why or why not?
4. How do vertical angles compare to adjacent angles?
5. How can you prove that vertical angles are always equal using the properties of intersecting lines?

**Tip:** Vertical angles are always congruent, meaning they have equal measures, regardless of the value of \(x\).

Learn how to solve a problem involving vertical angles where Angle 1 is expressed as 17x + 1 and Angle 2 as 20x - 14. Understand the concept of vertical angles and how to apply the Vertical Angles Theorem to find Angle 2. Suitable for Grades 7-9 students.

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