Proof:

To prove that the triangle is right-angled, we need to show that one of the angles is equal to 90 degrees.

Let's assume the three angles of the triangle are 3x, 7x, and 10x, where x is a constant.

Ratio of Angles:
The sum of all angles in a triangle is 180 degrees. Therefore, we can write the equation as:

3x + 7x + 10x = 180

Simplifying the equation, we get:

20x = 180

Dividing both sides of the equation by 20, we find:

x = 9

Angles of the Triangle:
Now, we can substitute the value of x back into the equation to find the angles of the triangle:

Angle 1 = 3x = 3 * 9 = 27 degrees
Angle 2 = 7x = 7 * 9 = 63 degrees
Angle 3 = 10x = 10 * 9 = 90 degrees

Conclusion:
Therefore, the angles of the triangle are 27 degrees, 63 degrees, and 90 degrees. Since one angle is equal to 90 degrees, the triangle is right-angled.

Visually Appealing Presentation:

Proof:
1. Ratio of Angles:
- Sum of all angles in a triangle is 180 degrees.
- Equation: 3x + 7x + 10x = 180
- Simplifying: 20x = 180
- x = 9

2. Angles of the Triangle:
- Angle 1 = 3x = 3 * 9 = 27 degrees
- Angle 2 = 7x = 7 * 9 = 63 degrees
- Angle 3 = 10x = 10 * 9 = 90 degrees

Conclusion:
- The angles of the triangle are 27 degrees, 63 degrees, and 90 degrees.
- Since one angle is equal to 90 degrees, the triangle is right-angled.

U take the angles as x y z