In a circle, two arcs of unequal length subtend angles in the ratio 5: 3. If the smaller angle is `45^@` then the measure of other angle in degrees is :

Options

A. `75^@`
B. `72^@`
C. `60^@`
D. `78^@`

Answer

To solve the problem step by step, we will follow the given information about the angles and their ratio.

### Step 1: Understand the Ratio of Angles
The problem states that the two angles subtended by the arcs are in the ratio of 5:3. Let's denote the angles as:
- Angle A = 5x
- Angle B = 3x

### Step 2: Identify the Smaller Angle
We are given that the smaller angle (Angle B) is 45 degrees. Therefore, we can set up the equation:
\[ 3x = 45^\circ \]

### Step 3: Solve for x
To find the value of x, we divide both sides of the equation by 3:
\[ x = \frac{45^\circ}{3} = 15^\circ \]

### Step 4: Calculate the Larger Angle
Now that we have the value of x, we can find the larger angle (Angle A):
\[ Angle A = 5x = 5 \times 15^\circ = 75^\circ \]

### Step 5: Conclusion
Thus, the measure of the other angle (the larger angle) is:
\[ \text{Angle A} = 75^\circ \]

### Final Answer
The measure of the other angle in degrees is **75 degrees**.

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