Two complementary angles are in the ratio `4:5`. Find the angles

Answer

To solve the problem of finding two complementary angles that are in the ratio of 4:5, we can follow these steps:

### Step 1: Define the angles
Let the first angle be \( 4x \) and the second angle be \( 5x \). Since the angles are complementary, their sum is \( 90^\circ \).

### Step 2: Set up the equation
According to the property of complementary angles:
\[ 4x + 5x = 90 \]

### Step 3: Combine like terms
Combine the terms on the left side:
\[ 9x = 90 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 9 to find \( x \):
\[ x = \frac{90}{9} = 10 \]

### Step 5: Find the angles
Now substitute \( x \) back into the expressions for the angles:
- First angle:
\[ 4x = 4 \times 10 = 40^\circ \]
- Second angle:
\[ 5x = 5 \times 10 = 50^\circ \]

### Step 6: Conclusion
The two complementary angles are \( 40^\circ \) and \( 50^\circ \).

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