Let's solve the problem step by step.

Information provided:

1. ABC is a straight line.
2. Angle BCD = 38°.
3. The reflex angle BCD = 250°.
4. We need to calculate the angle marked $x$.

Step 1: Relationship between angles on a straight line

The total angle around point $B$ on the straight line $ABC$ is $180^\circ$ because a straight line forms a straight angle.

Step 2: Reflex angle relationship

The reflex angle $BCD$ is given as $250^\circ$. This means the non-reflex angle $\angle DBC$ can be calculated as: $\text{Non-reflex angle } \angle DBC = 360^\circ - 250^\circ = 110^\circ.$

Step 3: Triangle $\triangle BCD$

The triangle $BCD$ has three angles:

• $\angle BCD = 38^\circ$,
• $\angle DBC = 110^\circ$,
• $\angle CBD = x$ (this is what we need to calculate).

The sum of angles in a triangle is always $180^\circ$, so: $x + 38^\circ + 110^\circ = 180^\circ.$

Simplify: $x = 180^\circ - (38^\circ + 110^\circ).$

$x = 180^\circ - 148^\circ = 32^\circ.$

Final Answer:

The angle $x$ is 32°.

Reasoning Summary:

1. The reflex angle was used to determine $\angle DBC = 110^\circ$.
2. Using the angle sum property of a triangle, $x$ was calculated.

Let me know if you'd like a detailed explanation for any step or have more questions! 😊

Related Questions:

1. How do you calculate reflex angles from non-reflex angles?
2. Why does the sum of angles in a triangle always equal $180^\circ$?
3. Can two angles in a triangle be reflex angles?
4. How is the concept of angles on a straight line used in geometry?
5. What are other examples where reflex angles are commonly used?

Tip:

Always remember that the sum of angles around a point is $360^\circ$, which can help in many geometry problems!