Final answer:
A triangle with an angle ratio of 3:5:7 is a scalene triangle, with angle measures of 36 degrees, 60 degrees, and 84 degrees respectively.
Step-by-step explanation:
When trying to determine whether a triangle is scalene, isosceles, equilateral, or obtuse-angled, one must understand that the sum of the angles in any triangle will always equal 180 degrees.
In the case of a triangle with angle ratios of 3:5:7, we can set up the following equation: 3x + 5x + 7x = 180. Simplifying this equation, (3+5+7)x = 15x = 180; therefore, x = 180/15 = 12 degrees. Substituting back, we have angles of 3x = 36 degrees, 5x = 60 degrees, and 7x = 84 degrees.
All the angles are different, and none of them are greater than 90 degrees, which identifies the triangle as a scalene triangle. This also means, the measures of the angles will be:
- 36 degrees
- 60 degrees
- 84 degrees