Chapter 7.3, Problem 12PSB

Solution

To Calculate: The number of sides need to add in the polygon, if the sum of its angle

increases by ${900}^o$ .

The number of sides added to the polygon would be $5$ .

Given information: Sum of the measures of the angles of a polygon is increased by 900.

Formula used: Sum of angles = ${180}^{\circ }(n-2)$

Calculation: Here, we are using the formula

Sum of angles = ${180}^{\circ }(n_1-2)$

➔Sum of angles + 900 = ${180}^{\circ }(n_2-2)$

Now, $900={180}^{\circ }(n_2-2)-{180}^{\circ }(n_1-2)$

➔ $\frac{900}{180}=n_2-n_1=5$

Hence, the number of sides need to add to the polygon would be $5$ .