College

If the measures of the angles of a triangle are represented by \(2x + 20\), \(x + 10\), and \(2x - 5\), what is the measure of the largest angle in the triangle?

1. 41
2. 46.5
3. 57
4. 82

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