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To solve parts (b) and (c) of this problem, we'll need to use the properties of cyclic quadrilaterals and angles subtended by the same arc in a circle.

### Recap of the Problem:
- Given:
  - \(\angle LQRT = 66^\circ\)
  - \(\angle LQST = 26^\circ\)
  - \(\angle PTS = 100^\circ\)

### Part (b): Finding \(\angle LTS\)
Since \( LQST \) is a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles in a cyclic quadrilateral sum up to \(180^\circ\).

\[
\angle LQST + \angle LTS = 180^\circ
\]

Given that \(\angle LQST = 26^\circ\), we can find \(\angle LTS\):

\[
\angle LTS = 180^\circ - 26^\circ = 154^\circ
\]

### Part (c): Finding \(\angle LTPS\)
To find \(\angle LTPS\), we use the fact that \( LTPS \) is a quadrilateral and the exterior angle at \(P\) is equal to the opposite interior angle \(LQT\). Therefore:

\[
\angle LTPS = \angle LQRT = 66^\circ
\]

So, the solutions are:
- **(b)** \(\angle LTS = 154^\circ\)
- **(c)** \(\angle LTPS = 66^\circ\)

Would you like more details or have any questions? Here are 5 related questions to expand your understanding:

1. How do you determine if a quadrilateral is cyclic?
2. Why do opposite angles of a cyclic quadrilateral add up to \(180^\circ\)?
3. How do you find the measure of an angle subtended by an arc in a circle?
4. What is the relationship between an exterior angle and the opposite interior angle in a cyclic quadrilateral?
5. Can the angle sum property of a quadrilateral be applied directly in this problem?

**Tip:** Always verify if a quadrilateral is cyclic before using properties specific to cyclic quadrilaterals.

Learn how to solve parts (b) and (c) of a problem involving angles in cyclic quadrilaterals. Includes detailed step-by-step solutions for finding angles LTS and LTPS. Suitable for high school students studying circle geometry.

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