Answer :
we are given the measures of three angles of a triangle in the form of polynomials. Let's remember that the sum of the angles of a triangles is always 180. Therefore, the sum of the three given polynomials must be 180, from there we can solve for "x", like this:
[tex](2x+20)+(x+10)+(2x-5)=180[/tex]We will add like terms, we get:
[tex]5x+25=180[/tex]subtracting 25 on both sides of the equation
[tex]\begin{gathered} 5x+25-25=180-25 \\ 5x=155 \end{gathered}[/tex]Now we divide by 5 on both sides of the equation
[tex]x=\frac{155}{5}=31[/tex]Now that we have the value of "x" we can replace it in the polynomials and find the largest of them, like this
[tex]\begin{gathered} 2x+20 \\ 2(31)+20=82 \end{gathered}[/tex][tex]\begin{gathered} x+10 \\ 31+10=41 \end{gathered}[/tex][tex]\begin{gathered} 2x-5 \\ 2(31)-5=57 \end{gathered}[/tex]Therefore, the largest angle is 82