Question

If the angles of a qudrilateral are x, (2x+13),(3x+10),(x-6) find x

Answer 1

Answer:

The sum of angles of a quadrilateral is 360°.

therefore,

x+2x+13+3x+10+x-6=360°

7x+17=360°

x=49

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Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Given :

• Angles are x, 2x + 13 , 3x + 10 , x - 6

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To Find :

• Value of x and value of all the angles

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Solution :

As we know that sum of all the four angles of a quadrilateral is 360° .

So, add all the angles and equate to 360° By angle sum property of a quadrilateral.

$\small \implies {\sf{x \: + \: 2x \: + \: 13 \: + \: 3x \: + \: 10 \: + \: x \: - \: 6 \: = \: 360}} \\ \\ \implies {\sf{7x \: + \: 23 \: - \: 6 \: = \: 360}} \\ \\ \implies {\sf{7x \: + \: 17 \: = \: 360}} \\ \\ \implies {\sf{7x \: = \: 360 \: - \: 17}} \\ \\ \implies {\sf{7x \: = \: 343}} \\ \\ \implies {\sf{x \: = \: \dfrac{343}{17}}} \\ \\ \implies {\sf{x \: = \: 49}}$

So, angles are :

• 1st Angle = x = 49
• 2nd Angle = 2x + 13 = 111
• 3rd Angle = 3x + 10 = 157
• 4th Angle = x - 6 = 43