Final answer:
The four angles given in the ratio 2:3:4:11 add up to 360 degrees, when considering the largest angle is 198 degrees. By finding each angle through the common factor, we verify they fit together at a point with no gaps.
Step-by-step explanation:
The student is asking about the ratio of angles that can fit together at a single point with no gaps. To show that the four angles fit together at a point, we must demonstrate that their sum is 360 degrees because that is the total number of degrees around a point. Given that the largest angle is 198 degrees and forms part of the ratio 2:3:4:11, we can find a common factor to determine the sizes of the other three angles.
First, we find the sum of the ratios which is 2+3+4+11 = 20. As the largest angle is 11 parts of the ratio and equals 198 degrees, each part of the ratio equals 18 degrees (198 degrees divided by 11). Multiplying each part of the ratio by 18 degrees, we get the four angles as follows:
- 2 parts x 18 degrees = 36 degrees
- 3 parts x 18 degrees = 54 degrees
- 4 parts x 18 degrees = 72 degrees
- 11 parts x 18 degrees = 198 degrees
Adding these angles together (36 + 54 + 72 + 198) confirms that they add up to 360 degrees, thus fitting together at a point with no gaps.