Question

Hello friends I have a question please solve this ☺️

The angles of a polygon are in the ratio of 3 : 6 : 12 : 12 : 12 : 12. Find the sum of interior angle and interior angles also ​

Answer 1

$\huge {\boxed {\boxed{ \pink {\mathcal{SOLUTION}}}}}$

$\: let \: the \: angles \: be \: x$

$\therefore \: \implies \: 3 x \: : \: 6x \: : \: 12x \: : \: 12x \: : \: 12x \:$

(Total sides = 5 hence, it is a pentagon)

$\green{The \: sum \: of \: interior \: angle \: of \: pentagon \: =}$

( x - 2) ×180°

=> ( 5 - 2) × 180°

=> 3 × 180°

= 540°

Each sides =

$\implies \: 3x + 6x + 12x + 12x + 12x = 540 \degree$

$\implies \: 45x = 540 \degree$

$\blue{Cross \: Multiplication }$

$\implies \: x = \dfrac{ \cancel{540}} {\cancel{45}}$

$\purple{(540 \: and \: 45 \: was \: the \: factor \: of 45 \:. \: So \: 540 \: got \: cancelled \: in \: 12th \: times \: and \: 45 \: in \: 1 \: time)}$

$\implies \: x \: = \: 12$

$\red{Interior \: angles = }$

$3x = 3 \times 12 = 36$

$6x = 6 \times 12 = 72$

$12 x = 12 \times 12 = 144$

$12x = 12 \times 12 = 144$

$12x = 12 \times 12 = 144$