Question

The angles of a quadrilateral are (4x°), (7x°), (15x°) and (10x°). Find the smallest and largest angles of the quadrilateral. ​

Answer 1

$\huge\boxed{\fcolorbox{red}{yellow}{Answer}}$

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Question:-

The angles of a quadrilateral are (4x°), (7x°), (15x°) and (10x°). Find the smallest and largest angles of the quadrilateral.

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Solution:-

$\sf{Sum~of~the~angles~of~a~quadrilateral~are~360°.}$

$\sf{so,~4x°~+~7x°~+~15x°~+~10x°~=~360°}$

$\sf\blue{[Angle~sum~property~of~triangle]}$

$\sf{→~36x°~=~360°}$

$\sf{→~x~=~{\dfrac{360}{10}}}$

$\sf{→~x~=~10°}$

$\sf\red{Smallest~angle~=~4x°~=~4~×~10~=~40°}$

$\sf\pink{Largest~angle~=~15x°~=~15~×~10~=~150°}$

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Answer 2

Answer:

The angles of a quadrilateral are (4x°), (7x°), (15x°) and (10x°). Find the smallest and largest angles of the quadrilateral.

Sum of the angles of a quadrilateral are 360°.

$4x° + 7x° + 15x° + 10x° = 360°$

$36x° = 360°$

$x = \frac{360}{10}$

$x = 10°$

$smallest \: angle \: = 4x° = 4 \times 10 = 40°$

$largest \: angle = 15x° = 15 \times 10 = 150°$

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