Let's call the measure of the larger angle as x, and the measure of the smaller angle as y.
When two angles are complementary, their sum is equal to 90º, therefore
[tex]x+y=90[/tex]The larger of the two is 30° more than twice the smaller, writing this as an equation, we have
[tex]x=2y+30[/tex]If we substitute this expression for x in the first equation, we have
[tex]\begin{gathered} (x)+y=90 \\ (2y+30)+y=90 \\ 2y+30+y=90 \\ 3y+30=90 \\ 3y=90-30 \\ 3y=60 \\ y=\frac{60}{3} \\ y=20 \end{gathered}[/tex]Using this y-value on the first expression, we have
[tex]\begin{gathered} x+(20)=90 \\ x+20=90 \\ x=90-20 \\ x=70 \end{gathered}[/tex]Then, the larger angle is 70º and the smaller angle is 20º.
