Question

How many degrees are there in an angle which equals two-third of its complement?

Answer 1

Let the required angle be x${}^{\circ }$.

Then its complementary angle = 90${}^{\circ }$ - x${}^{\circ }$

x${}^{\circ }$ = $\frac{2}{3}$ $\times$ 90${}^{\circ }$ - x${}^{\circ }$

3x${}^{\circ }$ = 180${}^{\circ }$ - 2x${}^{\circ }$

5x${}^{\circ }$ = 180${}^{\circ }$

x${}^{\circ }$ = 36${}^{\circ }$

Hence, there are 36 degrees in such an angle.