Question

Measures of two complementary angles (in degrees) are consecutive even integers. Find
the angles.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Angles}\mathrm{are}\mathrm{complementary}\mathrm{if}\mathrm{and}\mathrm{only}\mathrm{if}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{their}\mathrm{measures}\mathrm{is}90° \\ \mathrm{Let}\mathrm{two}\mathrm{consecutive}\mathrm{even}\mathrm{integers}\mathrm{be}\mathrm{n}\mathrm{and}\mathrm{n}+2 \\ \mathrm{Then},\mathrm{n}+\mathrm{n}+2=90 \\ 2\mathrm{n}+2=90 \\ 2\mathrm{n}=90-2 \\ 2\mathrm{n}=88 \\ \mathrm{n}=\frac{88}{2}=44 \\ \mathrm{Hence},\mathrm{the}\mathrm{two}\mathrm{complementary}\mathrm{angles}\mathrm{are}44°\mathrm{and}46° \end{gathered}$$

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