Respuesta :
Let the smallest angle be represented as
[tex]=x[/tex]Step 1: The largest angle of a triangle(let the largest angle =z) measures 9degrees less than 5 times the measure of the smallest angle, this statement is represented as
[tex]\begin{gathered} 5\text{ times the smallest angle gives} \\ =5\times x \\ =5x \\ 9\text{ degr}ees\text{ less will give the largest angle to be} \\ \text{largest angle =5x-}9 \\ z=5x-9 \end{gathered}[/tex]Step 2: let's calculate the middle angle (let the middle angle =y)
The middle angle measures three times that of the smallest angle, which means that
[tex]\begin{gathered} y=3\times x \\ \text{middle angle =y= 3x} \\ y=3x \end{gathered}[/tex]Recall that the total angles in a triangle give
[tex]=180^0[/tex]Therefore,
[tex]\begin{gathered} \text{largest angle + middle angle + smallest angle =180}^0 \\ z+y+x=180^0 \end{gathered}[/tex]Substituting we will have
[tex]\begin{gathered} 5x-9+3x+x=180^0 \\ \text{collect the sinmilar terms we will have} \\ 5x+3x+x=180^0+9^0 \\ 9x=189^0 \\ \text{divide both sides by 9} \\ \frac{9x}{9}=\frac{189^0}{9} \\ x=21^0 \end{gathered}[/tex]Hence,
the smallest angle is = 21 degrees
[tex]\begin{gathered} \text{The largest angle =5x-9} \\ =5\times21^0-9 \\ =105^0-9 \\ =96^0 \end{gathered}[/tex]Hence,
The largest angle = 96 degrees
[tex]\begin{gathered} \text{The middle angle=}3x \\ =3\times21^0 \\ =63^0 \end{gathered}[/tex]Hence,
The middle angle = 63 degrees
