To calculate the size of angle $x$, let us analyze the geometry of the triangle and the linear pair relationships:

1. The triangle contains angles $38^\circ$ and $101^\circ$. The third angle can be calculated since the sum of angles in a triangle is always $180^\circ$. $\text{Third angle} = 180^\circ - 38^\circ - 101^\circ = 41^\circ.$

2. Angle $x$ and the adjacent interior angle (the third angle we just calculated, $41^\circ$) form a straight line. The sum of angles on a straight line is $180^\circ$.

Thus, angle $x$ can be calculated as: $x = 180^\circ - 41^\circ = 139^\circ.$

Final Answer:

The size of angle $x$ is $139^\circ$.

Would you like a detailed breakdown of the geometric principles used, or do you have any further questions?

Related Questions:

1. Why is the sum of the angles in a triangle always $180^\circ$?
2. What is the difference between interior and exterior angles of a triangle?
3. How can we use linear pairs to solve other angle problems?
4. How do complementary and supplementary angles differ?
5. Can we apply the same principles to polygons with more than three sides?

Tip:

Remember, when solving geometry problems, always double-check for relationships like linear pairs, angle sums, and parallel lines to ensure accuracy!