Two positive angles whose measures have a sum of 180^(∘).
Adjacent
Two angles that share a common vertex and side.
∠ KJL and ∠ LJN
Practice makes perfect
Let's start by defining supplementary and adjacent angles.
Type of angle
Description
Supplementary
Two positive angles whose measures have a sum of 180^(∘).
Adjacent
Two angles that share a common vertex and blue
Now, let's consider the given diagram. According to the table, we are looking for pairs of angles with a common vertex, a common side, and whose measures add up to 180^(∘).
At first glance, it looks like there are no such angles. However, note that ∠ LJN is a right angle, as it is a sum of angles ∠ LJM and ∠ MJN.
m∠ LJN: & 56^(∘)+ 34^(∘)=90^(∘)
Now we know that m∠ LJN=90^(∘), note that it is adjacent another right angle ∠ KJL, as they share side JL and vertex J.
Since the sum of two right angles equals 180 ^(∘), the pair ∠ KJL and ∠ LJN is a pair of adjacent supplementary angles.
