The measures of the angles in a triangle have a ratio of 2: 9: 1. how do you find the measures of these angles

Hello. Firstly you have to remembet that the sum of the three angles in any triangle is 180grades
So, determining the constant (k) you will have:
2:9:1
2k+9k+1k=180
12k=180 180/12=k
k = 15
Multiply the constant by 180 and divide by the given ratio:
180*15 / 2
180*15 / 9 etc
then your angles are
2:9:1
24:108:12