Answer:
Smallest angle: 41°
Second angle: 57°
Third angle: 82°
Step-by-step explanation:
Let's call the smallest angle as [tex]x[/tex]
"while a third angle is twice the smallest": third angle is [tex]2x[/tex]
"One angle of a triangle measures 16∘ more than the smallest": 2nd angle is [tex]16+x[/tex]
We know sum of 3 angles in a triangle is 180 degrees, so we can set up the equation and solve for x:
[tex]x+(16+x)+(2x)=180\\x+16+x+2x=180\\4x=180-16\\4x=164\\x=\frac{164}{4}=41[/tex]
So smallest angle is 41°
The 2nd angle is 16+41=57°
third angle is 2*41=82°
