Two positive angles whose measures have a sum of 90^(∘).
Supplementary
Two positive angles whose measures have a sum of 180^(∘).
Adjacent
Two angles that share a common vertex and side.
Now, let's consider the given diagram.
To determine which pair or pairs of angles are complementary or supplementary, we will add each pair to determine their sums.
m∠ FGK + m∠ HGK: & 41^(∘)+ 131^(∘)=172^(∘)
m∠ GKL + m∠ HGK: & 49^(∘)+ 131^(∘)=180^(∘)
m∠ FGK + m∠ GKL: & 41^(∘)+ 49^(∘) =90^(∘)
Having checked all of the possible pairs of angles, we can conclude which angles have which type of relationship.
&∠ FGK and ∠ GKL are complementary.
&∠ GKL and ∠ HGK are supplementary.
Finally, ∠ FGK and ∠ HGK are adjacent angles as they share a common side KG and vertex G.
