To assist with angles in the given problems, I'll analyze the visible content and guide you through solving them using appropriate theorems related to circle geometry.

Problem 1: Inscribed Angle in a Circle

Description: There is a triangle inscribed in a circle with one angle marked, and the problem asks about the relationship between this angle and others in the circle.

Key Theorems:

1. Inscribed Angle Theorem: An angle inscribed in a circle is half the measure of the central angle that subtends the same arc.
2. Angles Subtended by the Same Arc: Angles subtended by the same arc at the circumference are equal.

Solution Approach:

• Identify the arc subtended by the given angle.
• Use the Inscribed Angle Theorem to find relationships between angles.

Problem 2: Intersecting Chords in a Circle

Description: This problem involves intersecting chords, and it likely asks for the angle formed by these chords.

Key Theorems:

1. Chord Angle Theorem: The angle between two intersecting chords is half the sum of the arcs they intercept.

Solution Approach:

• Calculate the arcs intercepted by the chords.
• Use the Chord Angle Theorem to find the angle.

Problem 3: Quadrilateral Inscribed in a Circle

Description: An inscribed quadrilateral is shown, and it seems to ask about the angles.

Key Theorem:

1. Opposite Angles of an Inscribed Quadrilateral: The opposite angles of a quadrilateral inscribed in a circle sum to $180^\circ$.

Solution Approach:

• Add the opposite angles and verify that their sum equals $180^\circ$.

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Please specify if you need the exact calculations or a particular problem to be worked out in detail. I'm here to clarify any questions or concepts!

Would you like more details on one of these problems?

Here are 5 more questions to consider:

1. Are there specific angles given that need solving?
2. Should I walk through the Inscribed Angle Theorem?
3. Do you need to find missing angles using arc measurements?
4. Are you familiar with opposite angles in cyclic quadrilaterals?
5. Is there a theorem that you find difficult to apply?

Tip: Always check if the angles you calculate make sense within the context of the circle, particularly for inscribed angles and intersecting chords.