The angles of a triangle are in the ratio 5 : 6 : 7 . Find each angle .

Answer

To find the angles of a triangle given in the ratio 5:6:7, we can follow these steps:

### Step 1: Set up the equation using a common factor
Let the common factor for the angles be \( x \). Therefore, we can express the angles as:
- First angle = \( 5x \)
- Second angle = \( 6x \)
- Third angle = \( 7x \)

### Step 2: Write the equation for the sum of angles in a triangle
The sum of the angles in a triangle is always \( 180^\circ \). Thus, we can write the equation:
\[ 5x + 6x + 7x = 180^\circ \]

### Step 3: Combine like terms
Combine the terms on the left side of the equation:
\[ (5x + 6x + 7x) = 18x \]
So, the equation becomes:
\[ 18x = 180^\circ \]

### Step 4: Solve for \( x \)
Now, divide both sides by 18 to find the value of \( x \):
\[ x = \frac{180^\circ}{18} = 10^\circ \]

### Step 5: Calculate each angle
Now, substitute \( x \) back into the expressions for each angle:
- First angle = \( 5x = 5 \times 10 = 50^\circ \)
- Second angle = \( 6x = 6 \times 10 = 60^\circ \)
- Third angle = \( 7x = 7 \times 10 = 70^\circ \)

### Final Answer
The angles of the triangle are:
- First angle: \( 50^\circ \)
- Second angle: \( 60^\circ \)
- Third angle: \( 70^\circ \)

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