Question

In a triangle, if the three angles are in the ratio \( 2 : 5 : 8 \), then the values of those three angles are:

• A. \( 24^\circ, 90^\circ, 66^\circ \)
• B. \( 96^\circ, 40^\circ, 44^\circ \)
• C. \( 24^\circ, 60^\circ, 96^\circ \)
• D. \( 60^\circ, 90^\circ, 30^\circ \)

Hint:

When the angles of a triangle are given in a ratio, use the property that the sum of angles in a triangle is always \( 180^\circ \) to find the angles.

Answer 1

The Correct Option is C

Step 1: Let the Angles be Proportional to a Variable We are told that the angles of the triangle are in the ratio \( 2 : 5 : 8 \). Let the angles be \( 2x, 5x, 8x \) where \( x \) is a common factor.

Step 2: Sum of Angles in a Triangle We know that the sum of the angles in any triangle is \( 180^\circ \). Therefore, we write: \[ 2x + 5x + 8x = 180^\circ \] Simplifying this: \[ 15x = 180^\circ \] Solving for \( x \): \[ x = \frac{180^\circ}{15} = 12^\circ \]

Step 3: Find the Angles Now that we know \( x = 12^\circ \), we can find the three angles by multiplying \( x \) with the respective ratios:
The first angle is \( 2x = 2 \times 12^\circ = 24^\circ \),
The second angle is \( 5x = 5 \times 12^\circ = 60^\circ \),
The third angle is \( 8x = 8 \times 12^\circ = 96^\circ \).


Step 4: Conclusion Therefore, the angles of the triangle are \( 24^\circ, 60^\circ, 96^\circ \).