https://file.aiquickdraw.com/mathbot/file/1728261476960aqp2ywq1.jpg

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 \(180^\circ\).

Learn how to calculate unknown angles (x) on a straight line in this geometry problem. Using the angle sum theorem and basic algebra, this example shows the detailed solution for solving both parts of the question. Suitable for Grades 7-9 students.

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