i. Let the measure of the complementary angle be x°.
35 + x = 90
∴35 + x-35 = 90 – 35 ….(Subtracting 35 from both sides)
∴x = 55
∴The complementary angle of 35° is 55°.
ii. Let the measure of the complementary angle be x°.
a + x = 90
∴a + x – a = 90 – a ….(Subtracting a from both sides)
∴x = (90 – a)
∴The complementary angle of a° is (90 – a)°.
iii. Let the measure of the complementary angle be x°.
22 + x = 90
∴22 + x – 22 = 90 – 22 ….(Subtracting 22 from both sides)
∴x = 68
∴The complementary angle of 22° is 68°.
iv. Let the measure of the complementary angle be a°.
40 – x + a = 90
∴40 – x + a – 40 + x = 90 – 40 + x ….(Subtracting 40 and adding x on both sides)
∴a = (50 + x)
∴The complementary angle of (40 – x)° is (50 + x)°.
