Answer:
To find the angles of the triangle when they are in the ratio of 1:2:7, you first need to determine the total ratio, which is \(1 + 2 + 7 = 10\). Then, you divide 360 degrees by this total ratio to find the value of each part of the ratio.
1. Degrees:
- \(1 \text{ part} \times \frac{360^\circ}{10} = 36^\circ\) (for the first angle)
- \(2 \text{ parts} \times \frac{360^\circ}{10} = 72^\circ\) (for the second angle)
- \(7 \text{ parts} \times \frac{360^\circ}{10} = 252^\circ\) (for the third angle)
2. Gradians:
- \(1 \text{ part} \times \frac{400 \text{ g}}{10} = 40 \text{ g}\) (for the first angle)
- \(2 \text{ parts} \times \frac{400 \text{ g}}{10} = 80 \text{ g}\) (for the second angle)
- \(7 \text{ parts} \times \frac{400 \text{ g}}{10} = 280 \text{ g}\) (for the third angle)
So, the angles of the triangle in degrees are \(36^\circ\), \(72^\circ\), and \(252^\circ\), and in gradians, they are \(40\text{ g}\), \(80\text{ g}\), and \(280\text{ g}\).
