At 5O'clock the hands of a clock make an obtuse angle and a reflex angle. Find the measure of each of the these angles

Answer

To find the obtuse and reflex angles formed by the hands of a clock at 5 o'clock, we can follow these steps:

### Step 1: Understand the position of the clock hands
At 5 o'clock, the minute hand is at the 12, and the hour hand is at the 5.

### Step 2: Calculate the angle between each hour mark
The clock is divided into 12 hours, and the total angle around the clock is 360 degrees. Therefore, the angle between each hour mark is:
\[ \text{Angle between each hour mark} = \frac{360 \text{ degrees}}{12} = 30 \text{ degrees} \]

### Step 3: Calculate the angle from 12 to 5
To find the angle from the 12 to the 5, we count the number of hour marks between them:
- From 12 to 1: 30 degrees
- From 1 to 2: 30 degrees
- From 2 to 3: 30 degrees
- From 3 to 4: 30 degrees
- From 4 to 5: 30 degrees

Thus, the total angle from 12 to 5 is:
\[ \text{Total angle} = 30 \text{ degrees} \times 5 = 150 \text{ degrees} \]

### Step 4: Determine the obtuse angle
The obtuse angle at 5 o'clock is the angle formed between the hour hand and the minute hand that is greater than 90 degrees. This angle is:
\[ \text{Obtuse angle} = 150 \text{ degrees} \]

### Step 5: Determine the reflex angle
The reflex angle is the angle that is greater than 180 degrees but less than 360 degrees. To find the reflex angle, we subtract the obtuse angle from 360 degrees:
\[ \text{Reflex angle} = 360 \text{ degrees} - 150 \text{ degrees} = 210 \text{ degrees} \]

### Final Answers:
- The obtuse angle at 5 o'clock is **150 degrees**.
- The reflex angle at 5 o'clock is **210 degrees**.

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