Question

Find the measures of the complementary angles of the following angles.

(i) 35^° (ii) a^° (iii) 22^° (iv) ${\left(40-x\right)}^{°}$

Answer 1

(i)
Let the measure of the complementary angle be a.
35 + a = 90
∴ a = 55°
Hence, the measure of the complement of an angle of measure 35° is 55°
(ii)
Let the measure of the complementary angle be x.
a + x = 90
∴ x = (90 − a)°
Hence, the measure of the complement of an angle of measure a° is (90 − a)°
(iii)
Let the measure of the complementary angle be a.
22 + a = 90
∴ a = 68°
Hence, the measure of the complement of an angle of measure 22° is 68°
(iv)
Let the measure of the complementary angle be a.
(40 − x) + a = 90
∴ a = (50 + x)°
Hence, the measure of the complement of an angle of measure (40 − x)° is (50 + x)°