Isosceles triangles have equal base angles.
The values of x and S are 7 and 32, respectively.
The base angles are given as: 15x - 31 and 9x + 11
So, we have:
[tex]\mathbf{15x - 31 = 9x + 11}[/tex]
Collect like terms
[tex]\mathbf{15x - 9x =31+ 11}[/tex]
[tex]\mathbf{6x =42}[/tex]
Divide both sides by 6
[tex]\mathbf{x =7}[/tex]
The measure of S is:
[tex]\mathbf{S = 180 - (15x - 31) - (9x + 11)}[/tex]
Substitute 7 for x
[tex]\mathbf{S = 180 - (15\times 7 - 31) - (9\times 7 + 11)}[/tex]
[tex]\mathbf{S = 180 - (74) - (74)}[/tex]
[tex]\mathbf{S = 32}[/tex]
Hence, the values of x and S are 7 and 32, respectively.
Read more about isosceles triangles at:
https://brainly.com/question/6238271
