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39 votes
Two angles are complementary. The larger of the two is 30° more than twice the smaller. Find the 2 angles

User Tiago Almeida
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1 Answer

12 votes
12 votes

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


x+y=90

The larger of the two is 30° more than twice the smaller, writing this as an equation, we have


x=2y+30

If we substitute this expression for x in the first equation, we have


\begin{gathered} (x)+y=90 \\ (2y+30)+y=90 \\ 2y+30+y=90 \\ 3y+30=90 \\ 3y=90-30 \\ 3y=60 \\ y=(60)/(3) \\ y=20 \end{gathered}

Using this y-value on the first expression, we have


\begin{gathered} x+(20)=90 \\ x+20=90 \\ x=90-20 \\ x=70 \end{gathered}

Then, the larger angle is 70º and the smaller angle is 20º.

User AlwaysLearn
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