Math, asked by shahidsahil1978, 8 months ago

In the given figure, find x.​

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Answers

Answered by thebrainlykapil
76

Answer: x = 28

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Solution :

  • Just use angle sum property ( A + B + C = 180°)
  • Fill what is given
  • Then solve it

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\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>to </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\:the\:</strong><strong>\</strong><strong>:</strong><strong> </strong><strong> Question :}} \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:</strong><strong>5x -60 \: + \: 2x+40 \: + \: 3x-80 \: = \: 180</strong><strong> </strong><strong> }} }\\ \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: </strong><strong>5x -60 \: + \: 2x+40 \: + \: 3x-80 \: = \: 180</strong><strong>\\ \\ \\\end{gathered}\end{gathered}

\sf\green{</strong><strong> </strong><strong>Rearrange</strong><strong> </strong><strong> \:</strong><strong> </strong><strong>the </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>equation</strong><strong> </strong><strong>}

\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: </strong><strong>5 x \:  +  \: 2 x \:   +  \: 3x \:  -  \: 60 \:  +  \: 40 \:  -  \: 80 \:  =  \: 180</strong><strong>\\ \\ \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: </strong><strong>1</strong><strong>0</strong><strong>x</strong><strong> \:  - </strong><strong>1</strong><strong>0</strong><strong>0</strong><strong> \:  =  \: 180\\ \\ \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 10x \:  =  \: 180</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>+</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>100</strong><strong>\\ \\ \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: </strong><strong>x \:  =  \:  \frac{280}{10} </strong><strong>\\ \\ \\\end{gathered}\end{gathered}

\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\</strong><strong>:</strong><strong> </strong><strong>x </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>2</strong><strong>8</strong><strong> }} }\\ \\\end{gathered}\end{gathered}

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Measure of angles

  • 5x-60 = 5 × 28 - 60 = 80°
  • 2x+40 = 2 × 28 + 40 = 96°
  • 3x-80 = 3 × 28 - 80 = 4°

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Verification:

  • ( angle sum property)

A + B + C = 180°

80 + 96 + 4 = 180°

\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:180° \: = \: 180°  }} }\\ \\\end{gathered}\end{gathered}

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