Question

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

(i) How many sides does it have?

(ii) What if the sum of outer angles is half the sum of inner angles?

(iii) If the sums are equal?

• A. (i) $3$ (ii) $4$ (iii) $6$
• B. (i) $6$ (ii) $4$ (iii) $3$
• C. (i) $4$ (ii) $3$ (iii) $6$
• D. (i) $3$ (ii) $6$ (iii) $4$

Answer 1

Answer: (D)

(i) $3$ (ii) $6$ (iii) $4$

$\left(i\right)$ Sum of interior angles of a polygon $=(n-2)\ast {180}^{\circ }$

Sum of exterior angles of a regular polygon $={360}^{\circ }$

$2(n-2)\ast {180}^{\circ }={360}^{\circ }$

$n-2=1\Rightarrow n=3$

$\left(ii\right)$ ${360}^{\circ }=\frac{1}{2}(n-2){180}^{\circ }$

$n-2=4\Rightarrow n=6$

$\left(iii\right)(n-2)\ast {180}^{\circ }={360}^{\circ }$

$n-2=2\Rightarrow n=4$