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To solve for the measure of angle \( x \) in the given triangle inscribed in a semicircle, we can use the properties of triangles and circles.

1. **Triangle in a Semicircle Property**:
   - Any triangle inscribed in a semicircle with one side as the diameter is a right triangle. This means one of its angles is 90°.

2. **Sum of Angles in a Triangle**:
   - The sum of the angles in any triangle is always 180°.

Given:
- One angle is 42°.
- The triangle is a right triangle, so another angle is 90°.

To find \( x \):

\[ x + 42° + 90° = 180° \]
\[ x + 132° = 180° \]
\[ x = 180° - 132° \]
\[ x = 48° \]

Therefore, the measure of angle \( x \) is 48°.

Do you want any more details or have any questions?

Here are five related questions you might ask:
1. How do you prove that a triangle inscribed in a semicircle is a right triangle?
2. What are the properties of inscribed angles in a circle?
3. Can this method be used for any triangle inscribed in a semicircle?
4. How would the problem change if the triangle were inscribed in a full circle instead of a semicircle?
5. What is the significance of the sum of angles in a triangle being 180°?

**Tip:** Always remember that a triangle inscribed in a semicircle with the hypotenuse as the diameter is a right triangle, which is a crucial property to solve such problems.

Learn how to solve for the measure of angle x in a triangle inscribed in a semicircle using key geometric properties. This problem involves the Triangle in a Semicircle Property, which states that any triangle inscribed in a semicircle with one side as the diameter is a right triangle. Suitable for students in Grades 9-12.

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