Find the values of x for which the angles `(2x-5)^(@)` and `(x-10)^(@)` are the complementary angles.

Explanation

To find the values of \( x \) for which the angles \( (2x - 5)^\circ \) and \( (x - 10)^\circ \) are complementary, we follow these steps:

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

### Step 2: Set up the equation
Since the angles \( (2x - 5)^\circ \) and \( (x - 10)^\circ \) are complementary, we can write the equation:
\[ (2x - 5) + (x - 10) = 90 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 2x - 5 + x - 10 = 90 \]
This simplifies to:
\[ 3x - 15 = 90 \]

### Step 4: Solve for \( x \)
Add \( 15 \) to both sides of the equation:
\[ 3x - 15 + 15 = 90 + 15 \]
This gives us:
\[ 3x = 105 \]

Now, divide both sides by \( 3 \):
\[ x = \frac{105}{3} \]
Calculating this gives:
\[ x = 35 \]

### Final Answer
The value of \( x \) is \( 35 \).

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