Question

Lindsay draws a right triangle and adds the measures of the right angle and one acute angle. Which is a possible sum of the two angles?

Answer 1

Anything between 91 degrees and 179 degrees. You can pick any between these two.

Answer 2

Answer:

$90< \gamma< 180$

Step-by-step explanation:

An acute angle is an angle that measures more than 0º and less than 90º. And a right angle is an angle that measures exactly 90º. Thus:

Let:

$\alpha = Right\hspace{3}angle=90^{\circ}\\\beta= Acute\hspace{3}angle\hspace{10}0^{\circ}<\beta<90^{\circ}\\\gamma= Sum\hspace{3} of\hspace{3} the\hspace{3} two\hspace{3} angles =\alpha +\beta$

So, in this sense, the sum of the two angles can´t be equal or greater than 180º, since $\beta<90^{\circ}$ , also it has to be at least greater than 90º since $\beta>0^{\circ}$

Therefore the sum of the two angles is:

$90^{\circ}< \gamma< 180^{\circ}$

In another words, the sum is greater than 90º and less than 180º