This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
90^\circ$$
Here are the solutions for questions 1, 2, and 3.
Question 1: Determine the value of the unknown variables in each of the diagram below.
Your solution for question 1 is correct.
Step 1: Identify angle . The angle (labeled as ) is subtended by the diameter at the circumference. The angle subtended by a diameter at any point on the circumference is .
Step 2: Identify angle . The sum of angles in a triangle is . In , the angles are , , and .
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Determine the value of the unknown variables in each of the diagram below. Your solution for question 1 is correct.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.