1.4 Some special angles
Complementary angles : If the sum of two
angles equals 90^{0} 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 nonadjacent complementary angles ( figure 1.20 b ).
Figure 1.20 a Figure
1.20 b
Since the measures of complementary angles always sum up to 90^{0} 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 = 30^{0}.
m Ð a + m Ð b = 90^{0}
30^{0} + m Ð b = 90^{0}
m Ð b = 90^{0}  30^{0}
m Ð b = 60^{0}
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 = 90^{0} and also
m Ð b + m Ð c = 90^{0}
\ m Ð a + m Ð c = m Ð b + m Ð c OR
m Ð a = m Ð b
