Answer
The smallest angle, $x,$ is $30^o.$ The largest angle, $x+80,$ is $110^o.$ And the third angle, $x+10,$ is $40^o.$
Work Step by Step
Let $x$ be the smallest angle. Then the largest angle is $x+80,$ and the third angle is $x+10.$
Since the sum of the measures of the angles of a triangle is $180^o,$ then
\begin{array}{l}\require{cancel}
x+(x+80)+(x+10)=180
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+x+80+x+10=180
\\
3x+90=180
\\
3x=180-90
\\
3x=90
\\
x=\dfrac{90}{3}
\\
x=30
.\end{array}
Hence, the smallest angle, $x,$ is $30^o.$ The largest angle, $x+80,$ is $110^o.$ And the third angle, $x+10,$ is $40^o.$
