It looks like you've uploaded an image related to circle theorems. The diagram includes labeled angles and geometric figures involving circles, tangents, and chords.

Let’s analyze each part of the diagram based on the angles and theorems typically related to circle geometry.

(n):

• Given angle $\angle b = 72^\circ$ inside the circle.
• This uses the theorem that states the angle at the center of a circle is twice the angle at the circumference subtended by the same arc. Therefore, angle $\angle d$ (at the center $O$) will be: $\angle d = 2 \times 72^\circ = 144^\circ$
• Angles $a$, $b$, and $c$ should follow standard properties of cyclic quadrilaterals, where opposite angles sum to $180^\circ$.

(q):

• Given angle $\angle z = 54^\circ$, this could imply the use of the alternate segment theorem or the fact that angles subtended by the same arc are equal.
• Since $\angle z = 54^\circ$, and if $x$ and $y$ are subtended by the same arc as $z$, they would be congruent.

(t):

• Given angles $\angle 60^\circ$ and $\angle 45^\circ$.
• The missing angle $x$ can be determined using the fact that the sum of angles in a triangle is $180^\circ$. So: $x = 180^\circ - 60^\circ - 45^\circ = 75^\circ$

Would you like further clarification or details on any particular circle theorem, or a step-by-step solution for one of these parts?

Here are 5 follow-up questions you might consider:

1. What is the relationship between angles in a semicircle?
2. How does the alternate segment theorem work in circle geometry?
3. How can you calculate angles subtended by the same arc?
4. How do opposite angles in a cyclic quadrilateral behave?
5. How does the angle subtended by a diameter of a circle behave?

Tip: When solving circle theorem problems, always identify whether the angles subtended are at the center or circumference, as this can significantly simplify your work!