Question

the angles of a quadrilateral are in the ratio 2:3:5:8. find the angles​

Answer 1

Answer:

2+3+5+8=18

then, sum if all angle of a quadrilateral is 360

then.360÷18= 20 .so all angles is 20.

Answer 2

$\mathbb{\bold{\underline{ANSWER}}}$

$\fbox{\textsf{40 ^{\textsf{o}} }, \textsf{60} ^{\textsf{o}} , \textsf{100} ^{\textsf{o}} \textsf{and} \textsf{160} ^{\textsf{o}} }$

$\mathbb{\bold{\underline{EXPLANATION:}}}$

$\textsf{Ratio of angles of Quadrilateral = 2 : 3 : 5 : 8}$

$\colon \to \textbf{To find the angles of the quadrilateral:}$

$\textsf{Since, the ratio of angles is [2 : 3 : 5 : 8], so,}$

$\star \textsf{ Let the angles of the quadrilateral be '2x', '3x', '5x' and '8x'}$

  $\bullet \textbf{ According to Angle Sum Property of Quadrilateral, the sum of} \\ \textbf{all angles in a quadrilateral is 360 ^{\textbf{o}} }}$

$\to \textsf{2x + 3x + 5x + 8x = 360}$

$\to \textsf{18x = 360}$

$\to \textsf{x = \frac{\textsf{360}}{\textsf{18}} = 20}$

$\therefore \textbf{\underline{x = 20}}$

$\textsf{If x = 20, then,}$

$\star \texttt{ 2x = 2 * 20 = \bold{40} }$

$\star \texttt{ 3x = 3 * 20 = \bold{60} }$

$\star \texttt{ 5x = 5 * 20 = \bold{100} }$

$\star \texttt{ 8x = 8 * 20 = \bold{160} }$

$\therefore \textbf{The angles of the quadrilateral are: 40 ^{\textsf{o}} , 60 ^{\textsf{o}} , 100 ^{\textsf{o}} and 160 ^{\textsf{o}} }$

$\colon \to \textbf{To verify the Angle Sum Property of the quadrilateral:}$

$\textsf{According to the above property, the sum of all angles of the quadrilateral} \\ \textsf{should be 360 ^{\textsf{o}} }}$

$\star \texttt{ Angles of quadrilateral are 40 ^{\texttt{o}} , 60 ^{\texttt{o}} , 100 ^{\texttt{o}} and 160 ^{\texttt{o}} }$

$\to \textsf{Sum of Angles \to 40 + 60 + 100 + 160} \\ \textsf{= 360}$

$\therefore \textbf{Angle Sum Property of Quadrilaterals is VERIFIED!}$