Do any of the figures show complementary, supplementary, or adjacent angles?
Figure 3
Practice makes perfect
The given figures will all show either complementary, supplementary, or adjacent angles. Let's first recall the definition of these three types of angles.
Type of angle
Description
Complementary
Two positive angles whose measures add to 90^(∘)
Supplementary
Two positive angles whose measures add to 180^(∘)
Adjacent
Two angles that share a common vertex and a side
Right away, we can see that the first and third figures show adjacent angles as their angles share a common side and have a common vertex.
However, we are looking for something common among three of the figures, not only two of them. Let's instead look at the sums of the angles in the figures to see if they are complementary or supplementary.
Figure 1:& ∠ 1+∠ 2=90^(∘)
Figure 2:& 50^(∘)+40^(∘)=90^(∘)
Figure 3:& ∠ 3+∠ 4= ?^(∘)
Figure 4:& 65^(∘)+25^(∘)=90^(∘)
Figures 1, 2, and 4 show complementary angles. Therefore, figure 3 does not belong.
