Question

In the given figure, find x.​

Answer 1

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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