Question

The sum S of the measures of the interior angles of a polygon with n sides is given by the formula S=180(n-2) The interior angles of a certain polygon have a sum of 1,620°. How many sides does the polygon have?

A: 11
B: 9
C: 13
D: 7

Answer 1

11

Solution -

Let the number of sides be n.

Now, according to the formula,

$\begin{aligned}1620 \degree & = 180 \degree(n - 2) \\ \\ \implies \: (n - 2) & = \frac{ {}^{9} \ \cancel{162} \cancel0 \degree}{_{1} \ \cancel{18} \cancel0 \degree} \\ \\ \implies \quad n - 2& = 9 \\ \\ \implies \qquad \quad n &= 11 \end{aligned}$

Hence, number of sides are 11.

Answer 2

Answer:

The number of sides is 11

Step-by-step explanation:

FIRSTLY

Apply your formula,Thus (n-2)×180 and add An equal to sign hence placing your result which is 1620 degrees to get or find your n being the number of sides .

CALCULATION

(n-2)× 180

placing an equal to sign

(n-2)× 180 = 1620

FURTHER CALCULATION

180n-360= 1620

180n= 1620 + 360

180n = 1980

180n/180 = 1980/180

n= 1980/180

n= 11

Hence your answer is 11