Question

Find the measures of the supplements of the following angles: 

i. 111° 

ii. 47° 

iii. 180° 

iv. (90 – x)°

Answer 1

i. Let the measure of the supplementary angle be x°. 

111 + x = 180 

∴ 111 + x – 111 = 180 – 111 …..(Subtracting 111 from both sides) 

∴ x = 69 

∴ The supplementary angle of 111° is 69°. 

ii. Let the measure of the supplementary angle be x°. 

47 + x = 180 

∴ 47 + x – 47 = 180 – 47 ….(Subtracting 47 from both sides) 

∴x = 133 

∴The supplementary angle of 47° is 133°. 

iii. Let the measure of the supplementary angle be x°. 

180 + x = 180 

∴180 + x – 180 = 180 – 180 ….(Subtracting 180 from both sides)

∴x = 0 

∴The supplementary angle of 180° is 0°. 

iv. Let the measure of the supplementary angle be a°. 

90 – x + a = 180 

∴ 90 – x + a – 90 + x = 180 – 90+ x ….(Subtracting 90 and adding x on both sides)

∴a = 180 – 90 + x 

∴a = (90 + x) 

∴The supplementary angle of (90 – x)° is (90 + x)°.