Question

The sum of interior angles of an equilateral triangle, a regular quadrilateral, a regular pentagon.....etc written as a sequence is

• A. ${90}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$
• B. ${360}^{\circ },{540}^{\circ },{720}^{\circ }\cdots \cdots$
• C. ${90}^{\circ },{180}^{\circ },{360}^{\circ }\cdots \cdots$
• D. ${180}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$

Answer 1

The correct option is D

${180}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$

The sum of interior angles of a n-sided regular polygon is given by $(n-2)\times {180}^{\circ }$.
Hence sum of interior angles of an equilateral triangle is ${180}^{\circ }$, a regular quadrilateral is ${360}^{\circ }$ and that of a regular pentagon is ${540}^{\circ }$.
Hence the corresponding sequence is given by:
${180}^{\circ },{360}^{\circ },{540}^{\circ }\cdots \cdots$