Question

(5) The sum of the outer angles of polygon is twice the
sum of the inner angles. How many sides does it have?
What if the sum of outer angles is half the sum of inner
angles? And if the sums are equal?​

Answer 1

$\large { \underline{ \sf { \red{ Given:- }}}}$

• The sum of the outer angles of polygon is twice the
• sum of the inner angles.

$\large { \underline{ \sf { \green{ To \: prove:- }}}}$

• What if the sum of outer angles is half the sum of inner angles?

$\large { \underline{ \sf { \orange{ Directions:- }}}}$

• The sum of the interiorof a regular polygon

➡️(2n-4)×90° (where n= number of sides)

• Sum of exterior angle of a regular polygon

➡️360°

$\sf \purple{According \: to \: question}$

$\implies{(2n-4)×90=2×360}$

$\implies{2n-4 = \frac{(2×360)}{90} }$

$\implies2n-4= 2×4$

$\implies{2n-4=8}$

$\implies{2n=8+4}$

$\implies2n=12$

$\implies{n = \frac{12}{2} }$

$\implies n = 6$

$\large \pink { \boxed{ \sf{ Hence, \: the \: polygon \: has \: 6 \: sides}}}$

$\large \pink { \boxed{ \sf{ </p><p>It \: means \: it \: is \: a \: regular \: hexagon.}}}$