To solve for the angles $t$ and the blue-marked angle in this circle-based geometry problem, let's analyze the provided information. Here's what we can observe:

1. Given Angles and Sides:
   • The angle on the left is marked as $94^\circ$.
   • Two pairs of sides are marked as equal, indicating isosceles triangles.
   • The shape is inscribed in a circle.

Step-by-Step Solution:

1. Angle Opposite Equal Sides:

   • Since the sides opposite to the angles $t$ and $94^\circ$ are equal, this suggests an isosceles triangle in which the base angles are equal.
   • Therefore, if we denote the angle opposite $94^\circ$ as $t$, we conclude $t = 94^\circ$.

2. Finding the Blue Angle:

   • Since we have a quadrilateral inscribed in a circle, we can apply the cyclic quadrilateral property, which states that opposite angles sum to $180^\circ$.
   • Thus, if one angle is $94^\circ$, its opposite angle (the blue-marked angle) must be $180^\circ - 94^\circ = 86^\circ$.

Summary of Results:

• Angle $t = 94^\circ$.
• Blue-marked angle = 86^\circ.

Would you like more details on any part of this solution, or have additional questions?

Here are 5 related questions to deepen understanding:

1. What are the properties of a cyclic quadrilateral?
2. How do we identify isosceles triangles in circle geometry?
3. Why do opposite angles in a cyclic quadrilateral add up to $180^\circ$?
4. Can these angle properties help in solving other circle-related problems?
5. How does the circle's inscribed angle theorem apply in similar cases?

Tip: Always remember that in a cyclic quadrilateral (a quadrilateral inscribed in a circle), opposite angles are supplementary (sum to $180^\circ$). This property often simplifies solving for unknown angles.