Fewpal
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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)°.

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