Question

Determine the measures of the angles of triangle DEF if the measures are in the ratio 1:1:16

Answer 1

The sum of all interior angles in a triangle is 180°, now, if we split that in (1+1+16) even pieces, that'd be 180 ÷ 18.

and then we give the ratio of 1, one of those pieces, the other ratio of 1, the same, and the ratio of 16, sixteen of those pieces.

$\bf 1:1:16\qquad \cfrac{180}{1+1+16}\implies \cfrac{180}{18}\implies 10\quad \qquad \stackrel{1}{10}~:~\stackrel{1}{10}~:~\stackrel{16}{160}$