Question

Match the following polygons with their respective sum of interior angles

• A. ${720}^{\circ }$
• B. ${180}^{\circ }$
• C. ${360}^{\circ }$
• D. ${540}^{\circ }$

Answer 1

The sum of interior angles of a polygon can be obtained by using the formula : $(n-2)\times {180}^{\circ }$ where $n=$ number of sides of the polygon .

1. Quadrilateral: $n=4$
$\Rightarrow$ $(n-2)\times {180}^{\circ }=(4-2)\times {180}^{\circ }$
$=2\times {180}^{\circ }$
=${360}^{\circ }$

2. Hexagon: $n=6$
$\Rightarrow$ $(n-2)\times {180}^{\circ }=(6-2)\times {180}^{\circ }$
$=4\times {180}^{\circ }$
=${720}^{\circ }$

3. Pentagon: $n=5$
$\Rightarrow$ $(n-2)\times {180}^{\circ }=(5-2)\times {180}^{\circ }$
$=3\times {180}^{\circ }$
=${540}^{\circ }$

4. Triangle: $n=3$
$\Rightarrow$ $(n-2)\times {180}^{\circ }=(3-2)\times {180}^{\circ }$
$=1\times {180}^{\circ }$
=${180}^{\circ }$