Question 1087233
three interior angles of a polygon are 160degres each.if the other interior angles are 120degres each,find the number of sides of the polygon?
<pre>Let the number of sides be n
Sum of INTERIOR angles of ANY POLYGON = 180(n – 2), or 180n - 360

The 3 INTERIOR angles measure 160<sup>o</sup> each, or sum to 3(160), or 480
The REMAINING number of sides = n – 3
The REMAINING INTERIOR angles measure 120<sup>o</sup> each, or sum to (n - 3)120, or 120n – 360
Sum of the INTERIOR angles of THIS POLYGON = 480 + 120n – 360

We then get: 180n – 360 = 480 + 120n - 360
180n - 360 = 120n + 120
180n – 120n = 120 + 360
60n = 480
n, or number of sides = {{{highlight_green(matrix(1,4, 480/60, or, 8, "(octagon)"))}}}

OR

Let the number of sides be S
Since 3 INTERIOR angles measure 160<sup>o</sup> each, each corresponding exterior angle measures 20<sup>o</sup> 
Total measure of the 3 corresponding EXTERIOR angles is: 3(20), or 60<sup>o</sup>  
Number of OTHER sides: S - 3
Since the other INTERIOR angles measure 120<sup>o</sup>  each, each of the OTHER corresponding exterior angles measures 60<sup>o</sup> (180 – 120)
Total measure of the OTHER corresponding EXTERIOR angles is: (S - 3)60, or 60S - 180

With the SUM of the EXTERIOR angles of a polygon being 360<sup>o</sup> , we get: 60 + 60S – 180 = 360
60S – 120 = 360
60S = 360 + 120
60S = 480
n, or number of sides = {{{highlight_green(matrix(1,4, 480/60, or, 8, "(octagon)"))}}}
ACCEPT no other answer.