Questions & Answers

Question

Answers

Answer

Verified

128.4k+ views

The adjective complementary is associated with the verb complete, "to fill up". An acute angle is "filled up" by its complement to form a right angle. The difference between an angle and a right angle is termed the complement of the angle.

The sum of two complementary angles is \[{90^ \circ }\].

let one of the angles be \[x\].

According to the question,

\[\begin{gathered}

\;\dfrac{2}{3}{\text{ }}of{\text{ }}x{\text{ }} + x = {\text{ }}90\; \\

\dfrac{{2x}}{3}{\text{ }} + x = 90\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }} \\

\dfrac{{(2x + 3x)}}{3} = {\text{ }}90\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }} \\

5x = {\text{ }}90 \times 3\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\; \\

x = {\text{ }}\dfrac{{270}}{5} \\

x = {\text{ }}54\;\;\;\;\;\;\;\;\;\;\; \\

\dfrac{2}{3} \times 54 = 36 \\

\end{gathered} \]

So, one angle is\[{36^ \circ }\] which is two third of its complement \[{54^ \circ }\]. They are Complementary angles.

\[\left( {36^\circ + 54^\circ = 90^\circ } \right)\]Therefore, the angle will be \[{36^ \circ }\] degree.