For an angle x°, find :(i) the complementary angle(ii) the supplement

1.	For an angle x°, find :(i) the complementary angle(ii) the supplementary angle(iii) the value of x° if its supplementary angle is three times its complementary angle.
Answer» For an angle x, (i) Complementary angle of x° = (90° – x) (ii) Supplementary angle of x° = (180° – x) (iii) ∵ ‘Supplementary angle = 3 (complementary anlge) 180°- x = 3 (90°-x) ⇒ 180°- x = 270°- 3x ⇒-x + 3x = 270°-180° ⇒ 2x = 90° ⇒x= (90/2)°= 45° ∴ x = 45°

For an angle x°, find :(i) the complementary angle(ii) the supplementary angle(iii) the value of x° if its supplementary angle is three times its complementary angle.

Answer»

For an angle x,

(i) Complementary angle of x° = (90° – x)

(ii) Supplementary angle of x° = (180° – x)

(iii) ∵ ‘Supplementary angle = 3 (complementary anlge)

180°- x = 3 (90°-x)

⇒ 180°- x = 270°- 3x

⇒-x + 3x = 270°-180°

⇒ 2x = 90°

⇒x= (90/2)°= 45°

∴ x = 45°