Question

if x = 55° then find the complementary , supplementary, and conjugate angles of x​

Answer 1

$~~~~~~\huge\sf\purple{\underline{\underline{UR \:ANSᏔER-}}}$

$~~~~~~~~~~~~~~\cal\red{Ꮤe\: Know\: That, }$

$~\sf\green{The\: sum\: of\: complementary \:angle\: is = 90}$

$~~~~~~~~~~~~~~~\green⟹$ 55+ y = 90

$~~~~~~~~~~~~~~~\green⟹$ y = 35°

$~~~~~~~~~\cal\red{And\: Ꮤe\: Also \:Know\: That,}$

$~\sf\green{The\: sum\: of\: supplementary \;angle = 180°}$

$~~~~~~~~~~~~~~\green⟹$ 55 + z = 180°

$~~~~~~~~~~~~~~\green⟹$ z = 180 - 55

$~~~~~~~~~~~~~~\green⟹$ z = 125°

$~~~~~~~~~~~~~~~~~~~~~\cal\red{And,}$

$~~\sf\green{Sum\:of \:conjugate\: angles = 360°}$

$~~~~~~~~~~~~~~\green⟹$ 55° +x = 360°

$~~~~~~~~~~~~~~\green⟹$ x = 360°-55°

$~~~~~~~~~~~~~~\green⟹$ x = 305°

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~hope it helps ❤

๑Ꮇαnσgnα

Answer 2

Given : - x = 55°

we need to find : - Complementary, supplementary , and conjugate angles of 'x' .

Theory : -

Complementary angles : These are the angles that sum up to 90°.

Supplementary angles : These are the angles that sum up to 180°.

Conjugate angles : These are the angles that sum up to 360°.

Solution : -

i)  a + 55° = 90°

 ⇒ a = 90° - 55°

  ⇒ a = 35°

∴ Complementary angle (a)  = 35°

ii) b + 55° = 180°

⇒ b = 180° - 55°

⇒ b = 125°

∴ Supplementary angle (b) = 125°

iii) c + 55° = 360°

⇒ c = 360° - 55°

  ⇒ c = 305°

∴ Conjugate angle (c) = 305°