Question

is it possible for a traingle to have angle measures in an extended ratio of 1 : 4 : 7?

Answer 1

if one angle is x and the ratio of 1 : 4 : 7, means second angle is 4x and third angle is 7x
since the sum of all three angles in a triangle is 180 degrees, we have

x+4x+7x=180
12x = 180
x = 15
then
4x = 60
7x = 105
The angles are 15°,60 °, and 105 °.
Therefore, yes.