An acute angle measures between 0^(∘) and 90^(∘). A right angle measures exactly 90^(∘). An obtuse angle measures between 90^(∘) and 180^(∘). A straight angle measures exactly 180^(∘).
Example Acute Angle: ∠ ABG
Example Right Angle: ∠ FGE
Example Obtuse Angle: ∠ ABC
Example Straight Angle: ∠ DGF
Practice makes perfect
There are four types of angles a.
Acute angle: 0^(∘) < a& < 90 ^(∘)
Right angle: a& = 90 ^(∘)
Obtuse angle: 90 ^(∘) < a& < 180 ^(∘)
Straight angle: a& = 180 ^(∘)
We are told in the previous exercise that ∠ DGF is a straight angle and that GB bisects ∠ DGF. From there, it follows that ∠ FGE and ∠ DGE are right angles.
Also, two exercises prior, we are told that m∠ ABC=112^(∘). By definition, this is an obtuse angle. Additionally, from the same exercise, we know that m∠ ABG =56^(∘). By definition, this is an acute angle.
