Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Question:}}}}}}}\end{gathered}$
If x = 55° then find the complementary , supplementary, and conjugate angles of x..
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Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• An angle x = 55°.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The complementary , supplementary, and conjugate angles of x.

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

We have , an angle x = 55°

The complementary of x,

Complementary angle are the angle in which sum of two angles is 90°.

x + y = 90°

➝ 55° + y = 90°

➝ y = 90° - 55°

➝ y = 35°

Hence, The complementary of x is 35°.

The supplementary of x,

Supplementary angle are the angle in which sum of two angles is 180°.

x + y = 180°

➝ 55° + y = 180°

➝ y = 180° - 55°

➝ y = 125°

Hence, The supplementary of x is 125°.

The conjugate of x,

Conjugate angle are the angle in which sum of two angles is 360°.

x + y = 180°

➝ 55° + y = 360°

➝ y = 360° - 55°

➝ y = 305°

Hence, The conjugate of x is 305°.

Answer 2

Question:-

➺if x = 55° then find the complementary supplementary and conjugate angles supplementary of x .

Given:-

➺x = 55

To Find:-

⇒complementary

⇒supplementary

⇒conjugate angle supplementary of x.

Analysis:-

➺sum of complementary angles = 90°

➺sum of supplementary angles = 180°

➺sum of conjugate angles= 360°

Solution:-

$\begin{gathered}\sf⟼ complementary \: angle \: of \: x = 90 = 55 \: \: \: \: \: \: \: \: \\ \\ \sf⟼complementary \: angle \: of \: x = 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \purple {\boxed{ \blue{ \: \: \: \: \: \therefore \: complement \: \: \: \: of \: \: \:\: \: x = 35 \: \: }}} \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf⟼supplement \: of \: angle \: x= 180 - 55 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf⟼supplement \: of \: \: angle \: x = 125 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \\ \\ \purple {\boxed{ \blue{ \: \: \: \: \: \therefore \: supplement \: \: \: \: of \: \: \:\: \: x = 125 \: \: }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf ⟼conjugate \: of \: supplement \: of \: x = 360 - 125 \\ \\ \sf⟼conjugate \: of \: supplement \: of \: x = 235 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \purple {\boxed{ \blue{ \: \: \: \: \: \therefore \:conjugate \: of supplement \: \: \: \: of \: \: \:\: \: x = 235 \: \: }}}\end{gathered}$

hope this helps.!