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Question

Find the measures of the complementary angles of the following angles.
(i) 35° (ii) a° (iii) 22° (iv) 40 - x°

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Solution

(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)°

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