Chapter 12.3, Problem 30E

To determine

To generate:the pattern by evaluating the expression $\left(n-2\right)·{180}^{\circ }$ for $n=3,4,5,6,7$ and describe the pattern.

Answer to Problem 30E

The pattern follows by this expression for is table of ${180}^{\circ }$ .

Explanation of Solution

Given : consider, the expressionprovided in the question,

  $\left(n-2\right)·{180}^{\circ }$ .

Calculation: for evaluating the expression substitute n by $3,4,5,6,7$ ,

  $\begin{array}{l}\left(n-2\right)·{180}^{\circ }=\left(3-2\right)·{180}^{\circ }\text{ [substitute n by 3]}\\ \left(n-2\right)·{180}^{\circ }={180}^{\circ }\text{ [subtract and multiply]}\\ \left(n-2\right)·{180}^{\circ }=\left(4-2\right)·{180}^{\circ }\text{ [substitute n by 4]}\\ \left(n-2\right)·{180}^{\circ }={360}^{\circ }\text{ [subtract and multiply]}\\ \left(n-2\right)·{180}^{\circ }=\left(5-2\right)·{180}^{\circ }\text{ [substitute n by 5]}\\ \left(n-2\right)·{180}^{\circ }={540}^{\circ }\text{ [subtract and multiply]}\\ \left(n-2\right)·{180}^{\circ }=\left(6-2\right)·{180}^{\circ }\text{ [substitute n by 6]}\\ \left(n-2\right)·{180}^{\circ }={720}^{\circ }\text{ [subtract and multiply]}\\ \left(n-2\right)·{180}^{\circ }=\left(7-2\right)·{180}^{\circ }\text{ [substitute n by 7]}\\ \left(n-2\right)·{180}^{\circ }={900}^{\circ }\text{ [subtract and multiply]}\end{array}$

The pattern follows by this expression is table of ${180}^{\circ }$ .

Hence, The pattern follows by this expression for is table of ${180}^{\circ }$