Question

the second angel im a triangle is 2° less the 3 times the first angle the third Angle is 14° more than twice the first angle find the measure of all three angles I'm the triangle (plz show step by step)

Answer 1

let's say the angles are "a", "b" and "c"


`\bf \begin{cases} \stackrel{first}{a}\\ \stackrel{second}{b}=\stackrel{\textit{2 less than 3 times \underline{a}}}{3a-2}\\ \stackrel{third}{c}=\stackrel{\textit{14 more than twice \underline{a}}}{2a+14} \end{cases} \\\\\\ \textit{now, the sum of all internal angles in a triangle is }180^o \\\\\\ a+b+c=\implies a+(3a-2)+(2a+14)=180 \\\\\\ 6a+12=180\implies 6a=180-12\implies 6a=168\implies a=\cfrac{168}{6} \\\\\\ a=28`


so a = 28°, plug that in "b" and "c", to see how much each is.