First slide

Arithmetic progression

Question

$The interior angles of a convex polygon forms on A.P with common$ $difference of 4^{\circ} . If the largest interior angle is 172^{\circ} then the number of sides is$

Moderate

A

10
B

11
C

12
D

8

Solution

Let n- be the number of sides of a polygon
$\begin{array}{l} t_{n} = a + (n - 1) d = 172 \\ \to a + 4 (n - 1) = 172 \\ \to a = 172 - 4 (n - 1) - \dots - (1) \\ S_{n} = \frac{n}{2} [a + 172] = (n - 2) (180) - - - (2) (\sin c e s u m o f t h e i n t e r i o r a n g l e s o f a' n' s i d e d p o l y g o n = (n - 2) 180^{°}) \\ From (1) and (2) \Rightarrow n = 12 . \end{array}$

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