Ashok has drawn an angle of measure `45^@27'` when he was asked to draw an angle of `45^@`. The percentage error in his drawing is

Options

A. `0.5% `
B. `1.0% `
C. `1.5%`
D. `2.0% `

Answer

To find the percentage error in Ashok's drawing of the angle, we will follow these steps:

### Step 1: Understand the given angle
Ashok was supposed to draw an angle of \( 45^\circ \) but he drew \( 45^\circ 27' \) (which means 27 minutes).

### Step 2: Convert the drawn angle into degrees
1 minute is equal to \( \frac{1}{60} \) degrees. Therefore, we need to convert 27 minutes into degrees:
\[ 27' = 27 \times \frac{1}{60} = \frac{27}{60} \text{ degrees} \]
Now, simplify \( \frac{27}{60} \):
\[ \frac{27}{60} = \frac{9}{20} \text{ degrees} \]

### Step 3: Calculate the total angle drawn by Ashok
Now, add this to the \( 45^\circ \):
\[ \text{Total angle drawn} = 45^\circ + \frac{9}{20}^\circ = 45 + 0.45 = 45.45^\circ \]

### Step 4: Calculate the error in the angle
The error in the angle is the difference between the angle drawn and the angle that was supposed to be drawn:
\[ \text{Error} = \text{Drawn angle} - \text{Actual angle} = 45.45^\circ - 45^\circ = 0.45^\circ \]

### Step 5: Calculate the percentage error
The percentage error is calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{\text{Error}}{\text{Actual Value}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.45}{45} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Error} = \left( \frac{0.45}{45} \right) \times 100 = 1\% \]

### Final Answer
The percentage error in Ashok's drawing is **1%**.

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