Let me analyze the geometry in the image and determine how to calculate the unknown angle $x$.

Analysis:

1. Angles provided:

   • 142°, 75°, 60° are given.
   • One right angle (90°) is marked.

2. Key observations:

   • The 142° angle is part of a straight line.
   • The sum of angles around a point or along a straight line should follow the rules of angle geometry.

Let me calculate $x$.

Step-by-Step Solution:

1. Calculate the angle adjacent to 142° (supplementary angle):

   • A straight line forms 180°, so: $\text{Adjacent angle to } 142° = 180° - 142° = 38°.$

2. Identify the triangle involving $x$:

   • In the triangle with $x$, the other two angles are $38°$ and $75°$.
   • The sum of the angles in a triangle is $180°$, so: $x + 38° + 75° = 180°.$
   • Simplify: $x = 180° - (38° + 75°) = 180° - 113° = 67°.$

Final Answer:

The value of $x$ is: $\boxed{67°}$

Would you like a detailed diagram of the solution steps or further clarification? Let me know!

Related Questions:

1. How do supplementary angles work?
2. How do you calculate unknown angles in a triangle?
3. Can you explain angle relationships in polygons?
4. How do right angles simplify geometric problems?
5. What is the importance of angle sums in geometry?

Tip:

Always check for supplementary and complementary angles when solving geometry problems—they often simplify the calculations!