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

`90< \gamma< 180`

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