Question

If two angles are supplementary to each other and angle in a radius 6:4 find the angle

Answer 1

Answer:

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Answer 2

$\sf\blue{Correct \ Question}$

$\sf{If \ two \ angles \ are \ supplementary \ to \ each}$

$\sf{other \ and \ angle \ in \ a \ ratio \ 6:4. \ Find}$

$\sf{the \ angles.}$

____________________________________

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ angles \ are \ 108^\circ \ and \ 72^\circ \ respectively. }$

$\sf\orange{Given:}$

$\sf{\implies{Angles \ are \ supplementary.}}$

$\sf{\implies{Angles \ are \ in \ ratio \ of \ 6:4}}$

$\sf\pink{To \ find:}$

$\sf{The \ angles.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ angles \ be \ x \ and \ y.}$

$\sf{According \ to \ the \ first \ condition. }$

$\sf{x+y=180...(1)}$

$\sf{According \ to \ the \ second \ condition. }$

$\sf{\frac{x}{y}=\frac{6}{4}}$

$\sf{\therefore{\frac{x}{y}=\frac{3}{2}}}$

$\sf{\therefore{2x=3y}}$

$\sf{\therefore{2x-3y=0...(2)}}$

$\sf{Multiply \ equation(1) \ by \ 3}$

$\sf{3x+3y=540...(3)}$

$\sf{Add \ equations \ (3) \ and \ (2)}$

$\sf{3x+3y=540}$

$\sf{+}$

$\sf{2x-3y=0}$

___________________

$\sf{\therefore{5x=540}}$

$\sf{\therefore{x=\frac{540}{5}}}$

$\boxed{\sf{\therefore{x=108}}}$

$\sf{Substitute \ x=108 \ in \ equation(1)}$

$\sf{108+y=180}$

$\sf{\therefore{y=180-108}}$

$\boxed{\sf{\therefore{y=72}}}$

$\sf\purple{\tt{\therefore{The \ angles \ are \ 108^\circ \ and \ 72^\circ \ respectively. }}}$