c One acute angle and one obtuse angle, one right angle and one acute angle, or two acute angles
D
d One acute and one obtuse angle, or two right angles
Practice makes perfect
a An acute angle is between 0^(∘) and 90^(∘). Let's draw an arbitrary acute angle as well as a ray in the interior of the angle.
Since the ray cuts the acute angle in two smaller angles, these have to be acute as well.
b A right angle is 90^(∘). Let's draw such an angle as well as a ray in the interior of it.
No matter how we draw the ray in the interior of the angle, the resulting angles will be less than 90^(∘) and are, therefore, acute.
c An obtuse angle is between 90^(∘) and 180^(∘). Let's draw an arbitrary obtuse angle as well as a ray in the interior of the angle.
Note that this is just one possibility. We could also draw the ray in the interior of the angle so we get one right angle and one acute. A third possibility is to draw the ray so we get one acute angle and one obtuse.
d A straight angle is 180^(∘). No matter how we draw the third ray, we will either get an acute angle and an obtuse angle or two right angles.
