Question

. The angles of a quadrilateral are in the ratio 3:6:9:2. Find each angle of the quadrilateral. [Hint: A quadrilateral is made up of 2 triangles.]​

Answer 1

$\large\underline{\underline\color{red}{☢{\pmb{\sf{ \: Given :-}}}}}$

• ➬ Ratios of the angles of quadrilateral = 3:6:9:2 .

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$\large\underline{\underline\color{red}{☢{\pmb{\sf{ \: To \: Find :-}}}}}$

• ➬ Find each of the angles .

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$\large\underline{\underline\color{red}{☢{\pmb{\sf{ \: Solution :-}}}}}$

⇝We know that :

$\blue\star{\underline{\text{\color{green}{ Sum of angles of a quadrilateral = 360°}}}}$

⇝Let :

• ➳ 1st angle = 3x
• ➳ 2nd angle = 6x
• ➳ 3rd angle = 9x
• ➳ 4th angle = 2x

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⇝Finding the angles :

${\twoheadrightarrow\sf {Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360°}}$

${\twoheadrightarrow\sf {3x+6x + 9x+ 2x = 360°}}$

${\twoheadrightarrow\sf {9x + 11x = 360°}}$

${\twoheadrightarrow\sf {20x = 360°}}$

${\twoheadrightarrow\sf {x =\cancel \frac{360}{20} }}$

$\large\orange{:\longmapsto{\sf{ x= {\green{\underline{\sf{ 18}}}}}}}$

⇝Angles :

$\large{\blue{:\leadsto{\pink{\tt{1st \: angle = 3x = 3 \times 18 = 54°}}}}}$

$\large{\blue{:\leadsto{\pink{\tt{2nd \: angle = 6x = 6 \times 18 = 108°}}}}}$

$\large{\blue{:\leadsto{\pink{\tt{3rd \: angle = 9x = 9 \times 18 = 162°}}}}}$

$\large{\blue{:\leadsto{\pink{\tt{4th \: angle = 2x = 2 \times 18 = 36°}}}}}$

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