The smallest angle in a triangle is 13 as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.The measures of the angles from smallest to biggest are °, °, and °.

First, lets assign a letter to each angle:a = smallest angleb = largest anglec = 3rd angle_____________________________________The question tells us the following:[tex]smallest\: angle=\frac{1}{3}\, largest\: angle[/tex]Therefore: [tex]largest\: angle = 3 \times smallest\: angle[/tex]We are also told:[tex]3rd\: angle=2\times smallest\: angle[/tex]_____________________________________Now lets form three equations by swapping out the angles with the correlating letter:[tex]a=\frac{1}{3}b[/tex][tex]b=3a[/tex][tex]c=2a[/tex]_______________________________________Remember, angles in a triangle add up to 180, so we can make another equation:[tex]a + b + c = 180[/tex]Now substitute in the values in terms of a, for b and c - and then solve for a.  (to solve the equation, everything has to be in the same terms, which is a in this case):[tex]a + b + c = 180[/tex][tex]a + 3a + 2a = 180[/tex][tex]6a = 180[/tex][tex]a = 30[/tex]___________________________________________Now that we know what a is, we can work out what b and c is, by substituting in the value of a into their equations:Value for b:[tex]b=3a[/tex][tex]b=3(30)[/tex][tex]b=90[/tex]Value for c:[tex]c=2a[/tex][tex]c=2(30)[/tex][tex]c=60[/tex]_______________________________________a = smallest angleb = largest anglec = 3rd angleSo:30 = smallest angle90 = largest angle60 = 3rd angle_________________________________________Answers:The measure of the angles from smallest to biggest are:30°,60°, and90°_________________________________________