Question

Find the measures of the supplements of the following angles.

(i) 111^° (ii) 47^° (iii) 180^° (iv) ${\left(90-x\right)}^{°}$

Answer 1

(i) 111^° (ii) 47^° (iii) 180^° (iv) ${\left(90-x\right)}^{°}$
(i)
Let the measure of the complementary angle be a.
111 + a = 180
∴ a = 69°
Hence, the measure of the complement of an angle of measure 111° is 69°
(ii)
Let the measure of the complementary angle be x.
47 + x = 180
∴ x = 133°
Hence, the measure of the complement of an angle of measure 47° is 133°
(iii)
Let the measure of the complementary angle be a.
180 + a = 180
∴ a = 0°
Hence, the measure of the complement of an angle of measure 180° is 0°
(iv)
Let the measure of the complementary angle be a.
(90 − x) + a = 180
∴ a = (90 + x)°
Hence, the measure of the complement of an angle of measure (90 − x)° is (90 + x)°