If the angles of a triangles are in the ratio of `2: 3: 5`, then find the ratio of the greatest angle to the smallest angle.
A `7:2` B `5:2` C `5:3` D `3: 5`

Options

A. D
B. C
C. A
D. B

Answer

To solve the problem of finding the ratio of the greatest angle to the smallest angle in a triangle where the angles are in the ratio of 2:3:5, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles in Terms of a Variable:**
Let the angles of the triangle be represented as:
- Angle 1 = 2x
- Angle 2 = 3x
- Angle 3 = 5x

2. **Set Up the Equation for the Sum of Angles:**
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ 2x + 3x + 5x = 180 \]

3. **Combine Like Terms:**
Combine the terms on the left side of the equation:
\[ 10x = 180 \]

4. **Solve for x:**
To find the value of x, divide both sides of the equation by 10:
\[ x = \frac{180}{10} = 18 \]

5. **Calculate the Angles:**
Now substitute the value of x back into the expressions for the angles:
- Angle 1 = \(2x = 2 \times 18 = 36\) degrees
- Angle 2 = \(3x = 3 \times 18 = 54\) degrees
- Angle 3 = \(5x = 5 \times 18 = 90\) degrees

6. **Identify the Greatest and Smallest Angles:**
From the calculated angles:
- Smallest angle = 36 degrees
- Greatest angle = 90 degrees

7. **Find the Ratio of the Greatest Angle to the Smallest Angle:**
The ratio of the greatest angle to the smallest angle is:
\[ \text{Ratio} = \frac{90}{36} \]

8. **Simplify the Ratio:**
To simplify \( \frac{90}{36} \):
- Divide both the numerator and denominator by 18:
\[ \frac{90 \div 18}{36 \div 18} = \frac{5}{2} \]

### Final Answer:
The ratio of the greatest angle to the smallest angle is \( \frac{5}{2} \).