Question

if the angles of a quadrilateral are 84 degree 120 degree and 36 degree. find the measure of the fourth angle?​

Answer 1

$\bold{ \underline{★ᴬᴺˢᵂᴱᴿ★}}$

• Fourth angle is 120°

$\bold{ \underline{Given :}}$

• Angles of a quadrilateral are 84° ; 120° ; and 36°.

$\bold{ \underline{To find :}}$

• Measure of the fourth angle ?

$\bold{ \underline{Solution :}}$

☯ Let the fourth angle 'y'

➥Sum of angles of a quadrilateral is 360°

$\small{ \bold{ \underline{★According \: to \: the \: question:}}}$

${\longrightarrow{84 + 120 + 36 + y \: = 240}}$

${\longrightarrow{240 + y = 360}}$

${\longrightarrow{y = 360−240 }}$

${ \longrightarrow{ \boxed{ \purple{y = 120 °}}}}★$

∴ Thus , Fourth angle is 120°

Answer 2

Answer:

We Should Know Some Trignometric Identities For Solving This Question.

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$\begin{gathered}1. \: \: \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) \\\end{gathered} </p><p>1.sin(2α)=2sin(α)cos(α)$

$2. \: \: \sin(180 - \alpha ) = \sin( \alpha )2.sin(180−α)=sin(α)$

$3. \: \: \sin(90 - \alpha ) = \cos( \alpha )3.sin(90−α)=cos(α)$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$L.H.S :- Sin10. Sin30. Sin50. Sin70$

$\begin{gathered}= \cos(90 - 10) \sin(30) \cos(90 - 40) \cos(90 - 70) \\ = \cos(80) \: \frac{1}{2} \: \cos(40) \: \cos(20) \\ = \frac{1}{4 \sin(20) } \cos(8 0 ) \cos(40) . \: 2 \sin(20) \cos(20) \\ = \frac{1}{8 \sin(20) } \cos(80) 2. \cos(40) \sin(40) \\ = \frac{1}{16 \sin(20) } 2 \cos(80) \sin(80 ) \\ = \frac{1}{16 \sin(20) } \sin(160) \\ = \frac{1}{16 \sin(20) } \sin(180 - 20) \\ = \frac{1}{16 \sin(20) } \sin(20) \\ = \frac{1}{16} \: \: \: \: \: \: \: \: .........R.H.S\end{gathered}$

$=cos(90−10)sin(30)cos(90−40)cos(90−70)$

$=cos(80) 2/1$

$cos(40)cos(20)= 4sin(20)1$

$cos(80)cos(40).2sin(20)cos(20)= 8sin(20)1$

$cos(80)2.cos(40)sin(40)= 16sin(20)1$

$2cos(80)sin(80)= 16sin(20)1$

$sin(160)= 16sin(20)1$

$sin(180−20)= 16sin(20)1$

$sin(20)= 16/1$

.........R.H.S,