To find the angles of a triangle when the measures are in an extended ratio such as 3:4:8, you can follow these steps:
1. **Understand the Extended Ratio**: The ratio 3:4:8 means that we can represent the angles of the triangle as 3x, 4x, and 8x, where x is a common multiplier.
2. **Use the Triangle Sum Theorem**: The sum of the angles in a triangle always equals 180 degrees. Therefore, you can write the equation:
3x + 4x + 8x = 180
3. **Simplify the Equation**: Combine like terms:
15x = 180
4. **Solve for x**: Divide both sides of the equation by 15:
x = 12
5. **Find Each Angle**: Now substitute x back into the expressions for each angle:
- First angle = 3x = 3(12) = 36 degrees
- Second angle = 4x = 4(12) = 48 degrees
- Third angle = 8x = 8(12) = 96 degrees
6. **Check Your Work**: Make sure the angles add up to 180 degrees:
36 + 48 + 96 = 180, which is correct!
Thus, the measures of the angles in the triangle are:
- First angle: 36 degrees
- Second angle: 48 degrees
- Third angle: 96 degrees