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.