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Let's solve the questions visible in the image.

### Question 5(a):
We have the following angles: \( 30^\circ \), \( 45^\circ \), and \( x \). The angles are at a point on a straight line.

- The sum of angles on a straight line is always \( 180^\circ \).
- Therefore, we can set up the equation:
  \[
  30^\circ + x + 45^\circ = 180^\circ
  \]
  Simplifying:
  \[
  75^\circ + x = 180^\circ
  \]
  \[
  x = 180^\circ - 75^\circ = 105^\circ
  \]
So, \( x = 105^\circ \).

---

### Question 5(b):
The angles given are \( 2x + 20^\circ \), \( 95^\circ \), and \( x + 10^\circ \), again at a point forming a straight line.

- The sum of angles on a straight line is \( 180^\circ \), so:
  \[
  (2x + 20^\circ) + 95^\circ + (x + 10^\circ) = 180^\circ
  \]
  Simplifying:
  \[
  2x + 20^\circ + 95^\circ + x + 10^\circ = 180^\circ
  \]
  \[
  3x + 125^\circ = 180^\circ
  \]
  Solving for \( x \):
  \[
  3x = 180^\circ - 125^\circ = 55^\circ
  \]
  \[
  x = \frac{55^\circ}{3} = 18.33^\circ
  \]
So, \( x = 18.33^\circ \).

---

### Question 5(c):
The triangle has one angle marked as \( 72^\circ \) and another angle marked as \( x \). We need to find \( x \).

- The sum of interior angles in a triangle is always \( 180^\circ \).
- Therefore, we can set up the equation:
  \[
  x + 72^\circ + 72^\circ = 180^\circ
  \]
  Simplifying:
  \[
  x + 144^\circ = 180^\circ
  \]
  \[
  x = 180^\circ - 144^\circ = 36^\circ
  \]
So, \( x = 36^\circ \).

---

Let me know if you want more details on these steps or if you have additional questions!

### Related Questions:
1. How do we calculate the sum of angles around a point?
2. Why do angles on a straight line always add up to \( 180^\circ \)?
3. What is the general rule for the sum of interior angles in a polygon?
4. How would you solve for \( x \) if the angles were part of a quadrilateral?
5. How can supplementary and complementary angles be applied to solve other problems?

### Tip:
When solving for angles, always check if they are on a straight line, around a point, or part of a polygon to apply the appropriate rule.

Determine the value of x in three given diagrams involving angles on a straight line and a triangle.

This problem involves determining the value of x in three different diagrams using basic geometric principles: angles on a straight line and the sum of interior angles in a triangle. Perfect for students in Grades 6-8.

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