Question

an exterior angle of a polygon is one-fourth of its interior angle. find number of sides​

Answer 1

Answer:

Exterior angle = x

Corresponding interior = y

Exterior angle = 1/4th of the interior

$x = \frac{y}{4}$

x + y = 180°

$\frac{y}{4} + y = 180$

y + 4y = 180°

5y = 180°

$y = \frac{180}{5}$

y = 36°

x = 180° - 36° = 144°

If each exterior angle of a polygon is A°

$side \: of \: the \: polygon = \frac{360}{a}$

Exterior angle = 36° so number of sides of polygon is,

$\frac{360}{36} = 10$

Sides of polygon = 10 sides

Answer 2

Heya mate!!

Exterior angle = x

Corresponding interior = y

Exterior angle = 1/4th of the interior

\begin{lgathered}x = \frac{y}{4} \\\end{lgathered}

x=

4

y

x + y = 180°

\frac{y}{4} + y = 180

4

y

+y=180

y + 4y = 180°

5y = 180°

y = \frac{180}{5}y=

5

180

y = 36°

x = 180° - 36° = 144°

If each exterior angle of a polygon is A°

side \: of \: the \: polygon = \frac{360}{a}sideofthepolygon=

a

360

Exterior angle = 36° so number of sides of polygon is,

\frac{360}{36} = 10

36

360

=10

Sides of polygon = 10 sides

Hope it helps u dear✌️✌️