Determine the value of the unknown variables in each of the diagram below.

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 $x$.
The angle $\angle ACB$ (labeled as $x$) is subtended by the diameter $AB$ at the circumference.
The angle subtended by a diameter at any point on the circumference is $90^\circ$.

$$x = 90^\circ$$

Step 2: Identify angle $y$.
The sum of angles in a triangle is $180^\circ$. In $\triangle ABC$, the angles are $x$, $y$, and $30^\circ$.

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