Answer: The measures of all the three angles are 24 , 60 and 96
Step-by-step explanation:
[tex]\\[/tex]Since the measures are given in ratio form, the first thing is to find the total ratio, which is
[tex]\\[/tex]2 + 5+ 8 = 15
[tex]\\[/tex]Recall that the sum of angles in a triangle is 180 ,so to calculate each angle , we have
[tex]\\[/tex]2/15 x 180 = 24
[tex]\\[/tex]also , 5/ 15 x 180 = 60
[tex]\\[/tex]Finally, 8/15 x 180 = 96
[tex]\\[/tex]The triangle is obtuse , since it is having one angle greater than 90.
[tex]\\[/tex]It can not be acute because of the existence of 96 , for a triangle to be acute , all the angles must be less than 90 , and it can not be right triangle because there is no existence of 90
