Given measure of an angle is 2/3 of it's complimentary angle. The measure of that angle is

Let [tex]\alpha[/tex] be an angle so that [tex]\beta[/tex] is its complementary angle.
We know that:
[tex]\alpha + \beta = 90^o[/tex]
Plugging in [tex]\alpha = \frac{2}{3} \beta[/tex] we get:
[tex]\frac{2}{3} \beta + \beta = 90^o \\ \frac{5}{3}\beta = 90^o \\ \beta = 54^o[/tex]
So our final answer is:
[tex]\alpha = \frac{2}{3}\beta = \frac{2}{3}(54^o) = 36^o[/tex]