question_answer

Find the angle which is \[\frac{2}{3}\] rd of its complement.

Answer:

Let the angle be x and its compliment be\[90{}^\circ -x\]  According to question,                       \[x=\frac{2}{3}({{90}^{\circ }}-x)\] \[x=\frac{2}{3}{{90}^{\circ }}-\frac{2}{3}x\]         \[x+\frac{2}{3}x={{60}^{\circ }}\] \[\frac{3x+2x}{3}={{60}^{\circ }}\]           \[5x={{180}^{\circ }}\] \[x=\frac{{{180}^{\circ }}}{5}={{36}^{\circ }}\]