Find the measures of the supplements of the following angles: i. 111�

1.	Find the measures of the supplements of the following angles: i. 111° ii. 47° iii. 180° iv. (90 – x)°
Answer» 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)°.

Find the measures of the supplements of the following angles: i. 111° ii. 47° iii. 180° iv. (90 – x)°

Answer»

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)°.