Find the measures of the complementary angles of the following angles

1.	Find the measures of the complementary angles of the following angles:i. 35° ii. a° iii. 22° iv. (40 – x)°
Answer» 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)°.

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

Answer»

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)°.

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