Let's go through the problems one by one:

1. Problem (a):

In the first image (a), we are dealing with two unknown angles, both marked as $x$, along with a known angle of $18^\circ$. The three angles form a straight line, which means their sum must be $180^\circ$. Thus, we can set up the equation:

$x + x + 18^\circ = 180^\circ$

Simplifying:

$2x + 18^\circ = 180^\circ$ $2x = 180^\circ - 18^\circ$ $2x = 162^\circ$ $x = \frac{162^\circ}{2} = 81^\circ$

So, for part (a), the value of $x$ is 81°.

2. Problem (b):

In the second image (b), we have two angles that form a straight line. The sum of the three angles (24°, $x$, and 36°) should also equal 180° because the angles form a straight line.

We set up the equation:

$24^\circ + x + 36^\circ = 180^\circ$

Simplifying:

$x + 60^\circ = 180^\circ$ $x = 180^\circ - 60^\circ = 120^\circ$

Thus, for part (b), the value of $x$ is 120°.

Let me know if you need further clarification or have additional questions!

Follow-up Questions:

1. Why is the sum of angles on a straight line always $180^\circ$?
2. Can you explain why we use algebraic equations to solve for $x$ in these problems?
3. How do alternate interior angles relate to this kind of problem-solving?
4. What other methods could be used to verify the angle calculations?
5. How does the sum of angles in a triangle compare to the sum of angles on a straight line?

Tip:

Remember that the sum of angles around a point always equals $360^\circ$, and the sum of angles on a straight line always equals $180^\circ$.