What approximate value will come in place of the question mark (?) in the following question? (You are not expected to calculate the exact value)
`8.02 – (? – 9.01) + (10.92)^2 = 120`

Options

A. 0
B. 18
C. 21
D. 24

Explanation

To solve the equation \( 8.02 - (? - 9.01) + (10.92)^2 = 120 \), we will approximate the values and simplify step by step.

### Step 1: Approximate the values
- Approximate \( 8.02 \) to \( 8 \) (since it is closer to 8).
- Approximate \( 9.01 \) to \( 9 \) (since it is very close to 9).
- Approximate \( 10.92 \) to \( 11 \) (since it is closer to 11).

### Step 2: Rewrite the equation
Substituting the approximated values into the equation gives us:
\[ 8 - (? - 9) + (11)^2 = 120 \]

### Step 3: Calculate \( (11)^2 \)
Calculate \( 11^2 \):
\[ 11^2 = 121 \]

### Step 4: Substitute back into the equation
Now substitute \( 121 \) back into the equation:
\[ 8 - (? - 9) + 121 = 120 \]

### Step 5: Simplify the equation
Combine the constants:
\[ 8 + 121 = 129 \]
So the equation becomes:
\[ 129 - (? - 9) = 120 \]

### Step 6: Isolate the term with the question mark
Rearranging gives:
\[ 129 - 120 = ? - 9 \]
\[ 9 = ? - 9 \]

### Step 7: Solve for the question mark
Adding \( 9 \) to both sides:
\[ 9 + 9 = ? \]
\[ ? = 18 \]

### Final Answer
The approximate value that will come in place of the question mark (?) is \( 18 \).

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