Angles of a Triangle in Ratio 2:7:11

To find the angles of a triangle in ratio 2:7:11, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

Step 1: Find the Sum of the Ratio

To find the sum of the ratio, we add the ratio numbers together: 2+7+11 = 20

Step 2: Find the Angle Measures

To find the angle measures, we need to multiply the ratio numbers by a constant factor that will make the sum of the products equal to 180 degrees.

Let's call this constant factor "x".

- The first angle measure is 2x
- The second angle measure is 7x
- The third angle measure is 11x

We can set up an equation to solve for x:

2x + 7x + 11x = 180

20x = 180

x = 9

Now, we can find the angle measures by multiplying each ratio number by 9:

- The first angle measure is 2x9 = 18 degrees
- The second angle measure is 7x9 = 63 degrees
- The third angle measure is 11x9 = 99 degrees

Conclusion

The angles of the triangle are 18 degrees, 63 degrees, and 99 degrees. We arrived at these angle measures by finding the sum of the ratio, setting up an equation with a constant factor, solving for x, and then multiplying each ratio number by x to find the angle measures.