How do you find each angle of a triangle if its angles are in the ratio 1:3:6?
1 = X Deg.
3 = 3x Deg,
6 = 6x Deg.
X + 3X + 6X = 180 Deg.
10X = 180,
X = 18 Deg.
3X = 3 * 18 = 54 Deg.
6X = 6 * 18 = 108 Deg.
You know their sum must add up to 180
let the angles be x, 3x and 6x
solve x + 3x + 6x = 180
sub the value of x back into the definitions
To find the measure of each angle in a triangle when the ratios of the angles are given, follow these steps:
1. Identify the ratio: In this case, the ratio of the triangle's angles is given as 1:3:6.
2. Determine the total ratio: To find the total ratio, add up the values in the given ratio. In this case, 1 + 3 + 6 = 10. This means that the total ratio of the triangle's angles is 10.
3. Calculate the value of each part: Divide each part of the ratio by the total ratio, and then multiply the result by 180° (since the sum of the angles in a triangle is always 180°).
- The first part of the ratio: 1/10 * 180° = 18°.
- The second part of the ratio: 3/10 * 180° = 54°.
- The third part of the ratio: 6/10 * 180° = 108°.
Therefore, each angle of the triangle measures 18°, 54°, and 108°, respectively.