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We are given a cyclic quadrilateral (with all four vertices on the circumference of a circle) in the diagram, and we need to find the values of \( p \) and \( q \).

### Key Information:
1. The angle of \( 132^\circ \) is provided at the top of the quadrilateral.
2. The angle at the bottom is \( 95^\circ \).
3. Angles \( p \) and \( q \) are to be found.
   
### Steps to Solve:

#### Step 1: Understanding properties of cyclic quadrilaterals
In any cyclic quadrilateral:
- Opposite angles are supplementary, meaning their sum is \( 180^\circ \).
  
For the angle \( 132^\circ \) at the top, the angle opposite to it is \( p \). Thus, using the property of supplementary angles:

\[
p + 132^\circ = 180^\circ
\]
\[
p = 180^\circ - 132^\circ = 48^\circ
\]

#### Step 2: Use the same property for the bottom angle
The angle \( q \) is opposite to \( 95^\circ \), so:

\[
q + 95^\circ = 180^\circ
\]
\[
q = 180^\circ - 95^\circ = 85^\circ
\]

Thus, the values are:
- \( p = 48^\circ \)
- \( q = 85^\circ \)

### Do you want more details or have any questions?

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Here are 5 related questions to explore:

1. What are the properties of cyclic quadrilaterals?
2. How do supplementary angles work in cyclic quadrilaterals?
3. Can we apply the same principles to non-cyclic quadrilaterals?
4. What are the implications of the angles summing to 180° in various quadrilaterals?
5. How would the solution change if the figure were not cyclic?

**Tip:** Always remember that opposite angles in a cyclic quadrilateral sum up to \( 180^\circ \), which helps solve many geometric problems quickly.

The diagram shows the side view drawing of Mr. Chong's house. It is found that the four vertices of the drawing lie on the circumference of a circle. Find the value of p and of q.

This problem involves determining the values of p and q in a cyclic quadrilateral where opposite angles sum to 180°. Learn the properties of cyclic quadrilaterals and how to apply the theorem to solve for unknown angles.

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