Explanation:

To determine the type of triangle based on the given ratio of angles, we need to find the values of the angles in the triangle.

Let the angles of the triangle be x, 2x, and 7x (where x is a constant factor).

According to the given ratio, we have the following equation:

x + 2x + 7x = 180 (Sum of angles in a triangle is 180 degrees)

Simplifying the equation, we get:

10x = 180

x = 18

So, the angles of the triangle are:

x = 18 degrees
2x = 36 degrees
7x = 126 degrees

Analysis of angles:

Now, let's analyze the values of the angles to determine the type of triangle.

1. Acute-angled triangle: An acute-angled triangle has all three angles less than 90 degrees.
- In this case, the angles are 18, 36, and 126 degrees, which includes one angle greater than 90 degrees (126 degrees), so it cannot be an acute-angled triangle.

2. Obtuse-angled triangle: An obtuse-angled triangle has one angle greater than 90 degrees.
- In this case, the angle 126 degrees is greater than 90 degrees, so it satisfies the condition for an obtuse-angled triangle.

3. Right-angled triangle: A right-angled triangle has one angle equal to 90 degrees.
- In this case, none of the angles are equal to 90 degrees, so it cannot be a right-angled triangle.

4. Right-angled isosceles triangle: A right-angled isosceles triangle has one angle equal to 90 degrees and two sides equal in length.
- In this case, none of the sides are equal in length, so it cannot be a right-angled isosceles triangle.

Therefore, based on the analysis of the angles, the given triangle is an obtuse-angled triangle (Option B).