Respuesta :
It is important to note that the sum of the measures of the interior angles of a triangle is 180°.
Based on the question, 4x - 1, 3x + 7, and 9x - 15 are the measures of the 3 angles of a triangle. Therefore, adding these three measures must sum up to 180°.
[tex](4x-1)+(3x+7)+(9x-15)=180[/tex]From the three angles mentioned, we don't know yet which one is the largest. For us to know, we need to get the value of x first.
So, to get the value of x, we can use the equation we wrote above.
[tex]\begin{gathered} \text{Eliminate the parenthesis.} \\ 4x-1+3x+7+9x-15=180 \\ \text{Combine similar terms.} \\ 16x-9=180 \\ \text{Add 9 on both sides.} \\ 16x-9+9=180+9 \\ 16x=189 \\ \text{Divide both sides by 16.} \\ \frac{16x}{16}=\frac{189}{16} \\ x=11.8125 \end{gathered}[/tex]Now that we have the value of x, let's plug this in to the 3 measures of angles and see which one is the largest.
[tex]4x-1=4(11.8125)-1=47.25-1=46.25[/tex][tex]3x+7=3(11.8125)+7=35.4375+7=42.4375[/tex][tex]9x-15=9(11.8125)-15=106.3125-15=91.3125[/tex]Therefore, the measure of the largest angle is 91.3125° or 91.31° when rounded off to the nearest hundredth.
