Angles of a Triangle in Ratio 2:7:11

To find the angles of a triangle in the ratio 2:7:11, we need to follow the steps given below:

Step 1: Add the ratio numbers (2+7+11) to get the total ratio value, which is 20.

Step 2: Divide each ratio number by the total ratio value and multiply by 180 degrees (sum of angles in a triangle) to get the measure of each angle.

2/20 x 180 = 18 degrees
7/20 x 180 = 63 degrees
11/20 x 180 = 99 degrees

Therefore, the angles of the triangle are 18 degrees, 63 degrees, and 99 degrees.

Explanation:

In a triangle, the sum of all angles is always 180 degrees. Let the angles of the triangle be 2x, 7x, and 11x (as per the given ratio). Then, we can write:

2x + 7x + 11x = 180
20x = 180
x = 9

Therefore, the angles of the triangle are:

2x = 2(9) = 18 degrees
7x = 7(9) = 63 degrees
11x = 11(9) = 99 degrees

We can check that the sum of these angles is indeed 180 degrees:

18 + 63 + 99 = 180

Hence, the angles of the triangle in the ratio 2:7:11 are 18 degrees, 63 degrees, and 99 degrees.