One of the quadrants of a circle is split into two equal sectors. What is the angle made at the center by each sector ?

Options

A. `90^(@)`
B. `180^(@)`
C. `45^(@)`
D. `30^(@)`

Answer

To solve the problem of finding the angle made at the center by each sector when one quadrant of a circle is split into two equal sectors, we can follow these steps:

### Step 1: Understand the Quadrant of a Circle
A circle is divided into four quadrants. Each quadrant represents a quarter of the circle.

**Hint:** Remember that a full circle is 360 degrees, and it is divided into four equal parts.

### Step 2: Calculate the Angle of One Quadrant
Since a full circle is 360 degrees, the angle of one quadrant is calculated as follows:
\[ \text{Angle of one quadrant} = \frac{360 \text{ degrees}}{4} = 90 \text{ degrees} \]

**Hint:** Each quadrant represents 1/4 of the total angle of the circle.

### Step 3: Split the Quadrant into Two Equal Sectors
Now, if we split one quadrant (which is 90 degrees) into two equal sectors, we need to divide the angle of the quadrant by 2:
\[ \text{Angle of each sector} = \frac{90 \text{ degrees}}{2} = 45 \text{ degrees} \]

**Hint:** When dividing an angle into equal parts, simply divide the total angle by the number of parts.

### Step 4: Conclusion
Thus, the angle made at the center by each sector when one quadrant is split into two equal sectors is:
\[ \text{Angle of each sector} = 45 \text{ degrees} \]

**Final Answer:** 45 degrees