ANSWER:
The angles are 63°, 45° and 72°
STEP-BY-STEP EXPLANATION:
We have the ratios and we know that the sum of all the internal angles within a triangle is equal to 180°.
Therefore, the measure of each angle will be equal to the ratio of each angle multiplied by 180, just like that
[tex]\begin{gathered} A\text{\degree=}\frac{a}{a+b+c}\cdot180 \\ B\text{\degree=}\frac{b}{a+b+c}\cdot180 \\ C\text{\degree=}\frac{c}{a+b+c}\cdot180 \\ \text{where a = 7, b = 5 and c = 8} \end{gathered}[/tex]Replacing in each case:
[tex]\begin{gathered} A\text{\degree=}\frac{7}{7+5+8}\cdot180=63\text{\degree} \\ B\text{\degree=}\frac{5}{7+5+8}\cdot180=45\text{\degree} \\ C\text{\degree=}\frac{8}{7+5+8}\cdot180=72\text{\degree} \end{gathered}[/tex]