Electric field equation incorporated with momentum equation
Answers
AnswEr :
\begin{lgathered}\bold{Given}\begin{cases}\sf{Angle_1=(x-35)\degree} \\ \sf{Angle_2=(x-25)\degree}\\ \sf{Angle_3=\bigg(\dfrac{1}{2}x-10\bigg)\degree}\\\sf{Find\:the\:value\:of\:x?}\end{cases}\end{lgathered}
Given
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Angle
1
=(x−35)°
Angle
2
=(x−25)°
Angle
3
=(
2
1
x−10)°
Findthevalueofx?
• Let's Head to the Question Now :
\begin{lgathered}\longrightarrow \tt Sum \: of \: Angles \: of \:Triangle = 180\degree \\ \\ \longrightarrow \tt Angle_1 + Angle_2 + Angle_3 = 180 \\ \\ \longrightarrow \tt(x - 35) + (x - 25) + \bigg( \dfrac{1}{2}x - 10 \bigg) = 180\degree \\ \\ \longrightarrow \tt x - 35 + x - 25+ \dfrac{x}{2} - 10 = 180 \\ \\ \longrightarrow \tt \bigg(x + x + \dfrac{x}{2} \bigg) - 35 - 25 - 10 = 180 \\ \\ \longrightarrow \tt \bigg( \dfrac{2x + 2x + x}{2} \bigg) - 70 = 180 \\ \\ \longrightarrow \tt \dfrac{5x }{2} = 180 + 70 \\ \\ \longrightarrow \tt \dfrac{5x}{2} = 250 \\ \\ \longrightarrow \tt x = \cancel{250} \times \dfrac{2}{ \cancel5} \\ \\ \longrightarrow \tt x =50 \times 2 \\ \\ \longrightarrow \boxed{ \red{\tt x =100\degree}}\end{lgathered}
⟶SumofAnglesofTriangle=180°
⟶Angle
1
+Angle
2
+Angle
3
=180
⟶(x−35)+(x−25)+(
2
1
x−10)=180°
⟶x−35+x−25+
2
x
−10=180
⟶(x+x+
2
x
)−35−25−10=180
⟶(
2
2x+2x+x
)−70=180
⟶
2
5x
=180+70
⟶
2
5x
=250
⟶x=
250
×
5
2
⟶x=50×2
⟶
x=100°
⠀
∴ Therefore, Value of x will be 100°.
• V E R I F I C A T I O N :
\begin{lgathered}\Longrightarrow \tt Sum \: of \: Angles \: of \:Triangle = 180\degree \\ \\ \Longrightarrow \tt Angle_1 + Angle_2 + Angle_3 = 180 \\ \\ \Longrightarrow \tt(x - 35) + (x - 25) + \bigg( \dfrac{1}{2}x - 10 \bigg) = 180\degree \\ \\ \Longrightarrow \tt(100 - 35) + (100 - 25) + \bigg( \cancel\dfrac{100}{2} - 10 \bigg) = 180\degree \\ \\ \Longrightarrow \tt65+75 +(50 - 10) = 180\degree \\ \\ \Longrightarrow \tt140+40 = 180\degree \\ \\ \Longrightarrow \blue{ \tt 180\degree= 180\degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\underline\frak{Hence,\: Verified}\end{lgathered}
⟹SumofAnglesofTriangle=180°
⟹Angle
1
+Angle
2
+Angle
3
=180
⟹(x−35)+(x−25)+(
2
1
x−10)=180°
⟹(100−35)+(100−25)+(
2
100
−10)=180°
⟹65+75+(50−10)=180°
⟹140+40=180°
⟹180°=180°
Hence,Verified