To solve this problem, let's break down the given information:

1. Given:

   • $\angle 1$ and $\angle 2$ form a linear pair.
   • $m\angle 1 = 18x - 1$
   • $m\angle 2 = 23x + 17$

2. Concept:
   Since $\angle 1$ and $\angle 2$ form a linear pair, their measures add up to 180°: $m\angle 1 + m\angle 2 = 180$

3. Equation Setup:
   Substitute the expressions for $m\angle 1$ and $m\angle 2$ into the equation: $(18x - 1) + (23x + 17) = 180$

4. Combine Like Terms: $18x + 23x - 1 + 17 = 180$ $41x + 16 = 180$

5. Solve for $x$: $41x = 180 - 16$ $41x = 164$ $x = \frac{164}{41} = 4$

6. Find $m\angle 2$:
   Substitute $x = 4$ into the expression for $m\angle 2$: $m\angle 2 = 23x + 17$ $m\angle 2 = 23(4) + 17$ $m\angle 2 = 92 + 17 = 109$

Answer:

The measure of $m\angle 2$ is 109°.

Would you like further details on this solution, or do you have any questions?

Related Questions

1. What is the measure of $m\angle 1$ in this problem?
2. How do we determine if two angles form a linear pair?
3. What properties do linear pairs have in geometry?
4. How would the solution change if the sum of the angles were not 180°?
5. How can we verify if our solution for $x$ is correct?

Tip:

For angles in a linear pair, always remember they are supplementary, meaning their measures add up to 180°.