If `(2x+17)^(@),(x+4)^(@)` are complementary, find x :

Options

A. `63^(@)`
B. `53^(@)`
C. `35^(@)`
D. `23^(@)`

Answer

To solve the problem where the angles \( (2x + 17)^\circ \) and \( (x + 4)^\circ \) are complementary, we follow these steps:

### Step 1: Understand the definition of complementary angles
Complementary angles are two angles whose sum is equal to \( 90^\circ \).

### Step 2: Set up the equation
Given the angles \( (2x + 17)^\circ \) and \( (x + 4)^\circ \), we can write the equation:
\[ (2x + 17) + (x + 4) = 90 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 2x + 17 + x + 4 = 90 \]
This simplifies to:
\[ 3x + 21 = 90 \]

### Step 4: Isolate the variable \( x \)
Subtract \( 21 \) from both sides:
\[ 3x = 90 - 21 \]
\[ 3x = 69 \]

### Step 5: Solve for \( x \)
Divide both sides by \( 3 \):
\[ x = \frac{69}{3} \]
\[ x = 23 \]

### Final Answer
Thus, the value of \( x \) is \( 23 \).

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