Question

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?1 412) 46.53) 574) 82

Answer 1

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:

`(2x+20)+(x+10)+(2x-5)=180`

We will add like terms, we get:

`5x+25=180`

subtracting 25 on both sides of the equation

`\begin{gathered} 5x+25-25=180-25 \\ 5x=155 \end{gathered}`

Now we divide by 5 on both sides of the equation

`x=(155)/(5)=31`

Now that we have the value of "x" we can replace it in the polynomials and find the largest of them, like this

`\begin{gathered} 2x+20 \\ 2(31)+20=82 \end{gathered}`
`\begin{gathered} x+10 \\ 31+10=41 \end{gathered}`
`\begin{gathered} 2x-5 \\ 2(31)-5=57 \end{gathered}`

Therefore, the largest angle is 82