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

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Find the measures of the complementary angles of the following angles:

i. 35°

ii. a°

iii. 22°

iv. (40 – x)°

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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)°.