The problem you provided involves three lines intersecting at a single point, forming several angles. The task is to determine the value of angle $\alpha$ based on the given angles of $40^\circ$ and $60^\circ$.

Solution:

The key to solving this problem is to recognize that the angles around a point sum up to $360^\circ$. Since $\alpha$ is adjacent to both $40^\circ$ and $60^\circ$, we need to use the fact that the sum of the angles on a straight line (which forms a linear pair) is $180^\circ$.

Given:

• One angle is $40^\circ$.
• Another angle is $60^\circ$.

The unknown angle $\alpha$ can be found as follows:

1. The straight line formed with $\alpha$ and the $60^\circ$ angle will sum to $180^\circ$: $\alpha + 60^\circ = 180^\circ$ $\alpha = 180^\circ - 60^\circ = 120^\circ$

Thus, the correct answer for $\alpha$ is $120^\circ$.

However, since the question asks for the measure of $\alpha$ in the provided multiple-choice format, it seems that we need to verify if one of the provided options matches $120^\circ$.

Answer:

The correct value of angle $\alpha$ should be $120^\circ$, but since this value is not listed in the options, it suggests that there may have been a misunderstanding of the angles provided, or an alternative method is needed based on the choices provided.

Please review the options or provide additional information to adjust the solution accordingly. If you need any further details or clarification, let me know!

Would you like to ask anything more about this problem, or do you want to explore any related topics? Here are some potential follow-up questions:

1. What are supplementary angles, and how are they used in geometry?
2. How can you determine the value of an unknown angle in different geometrical configurations?
3. What other geometric properties apply to intersecting lines?
4. How do we find the angles formed by parallel lines intersected by a transversal?
5. Can you explain how to verify angle measurements using a protractor?

Tip: Always double-check the sum of angles around a point to ensure accuracy in solving geometry problems.