In a circle with centre P, AB is a minor arc. Point Ris a point other than A and B on major arc `if ANGLE /_APB = 150^(@).` then `angle ARB=`.........

Options

A. `150^(@)`
B. `75^(@)`
C. `50^(@)`
D. `100^(@)`

Answer

To solve the problem, we will use the properties of angles in a circle. Specifically, we will use the relationship between the angle subtended at the center of the circle and the angle subtended at any point on the circumference.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have a circle with center P.
- AB is a minor arc.
- R is a point on the major arc (not on AB).
- The angle ∠APB = 150°.

2. **Understand the Relationship Between Angles:**
- The angle subtended at the center of the circle (∠APB) is related to the angle subtended at any point on the circumference (∠ARB) by the formula:
\[ \text{Angle subtended at center} = 2 \times \text{Angle subtended at circumference} \]
- This means:
\[ \angle APB = 2 \times \angle ARB \]

3. **Substitute the Known Value:**
- We know that ∠APB = 150°.
- Therefore, we can write:
\[ 150° = 2 \times \angle ARB \]

4. **Solve for ∠ARB:**
- To find ∠ARB, divide both sides of the equation by 2:
\[ \angle ARB = \frac{150°}{2} = 75° \]

5. **Conclusion:**
- Thus, the angle ∠ARB is 75°.

### Final Answer:
\[ \angle ARB = 75° \]