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

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Find the measures of the supplements of the following angles:

i. 111°

ii. 47°

iii. 180°

iv. (90 – x)°

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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)°.