∠1 and ∠2 are vertical angles.  If *m*∠1=(17x+1) and *m*∠2=(20x – 14), find *m*∠2.

Vertical angles are congruent, meaning they have equal measures. Therefore, we can set the expressions for \( m \angle 1 \) and \( m \angle 2 \) 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:

\[
x = 5
\]

Now that we have the value of \( x \), we can find the measure of \( m \angle 2 \):

\[
m \angle 2 = 20x - 14 = 20(5) - 14 = 100 - 14 = 86^\circ
\]

So, the measure of \( m \angle 2 \) is \( 86^\circ \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. If \( m \angle 3 = 3x + 10 \) and \( m \angle 4 = 5x - 20 \), what is the measure of \( m \angle 4 \) if they are vertical angles?
2. What are vertical angles, and why are they always equal?
3. Solve for \( x \) if \( m \angle 5 = 7x + 2 \) and \( m \angle 6 = 10x - 8 \), assuming \( \angle 5 \) and \( \angle 6 \) are vertical angles.
4. How does the concept of vertical angles apply in real-world scenarios, like architecture?
5. If two angles are supplementary and one is given by \( 12x + 5 \), what is the measure of the other angle?

**Tip:** When solving for unknowns in angle problems, always look for relationships like congruence, supplementary, or complementary angles to set up equations correctly.

Learn how to solve a problem involving vertical angles. Understand the Vertical Angles Theorem and apply it to find the measure of angle 2 given angle 1's measure is defined by an expression. Suitable for Grades 7-9.

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