1.4 Some special angles
Complementary angles : If the sum of two
angles equals 900 the two angles are called complementary.
Complementary angles thus add up to a right angle.
Complementary angles are of two types. If they have one side in common they are called adjacent complementary angles ( figure 1.20 a ). If no side is common then they are called non-adjacent complementary angles ( figure 1.20 b ).
Figure 1.20 a Figure
Since the measures of complementary angles always sum up to 900 if the measure of one angle is known that of the complement can be found easily. In figure 1.20 b Ð a and Ð b are complementary. Also it is known that m Ð a = 300.
m Ð a + m Ð b = 900
300 + m Ð b = 900
m Ð b = 900 - 300
m Ð b = 600
Theorem : If two angles are complementary to a third angle, then they are equal to each other.
Proof : Ð a and Ð b are both complementary to Ð c.
\ m Ð a + m Ð c = 900 and also
m Ð b + m Ð c = 900
\ m Ð a + m Ð c = m Ð b + m Ð c OR
m Ð a = m Ð b