Answer:
x = 7
Explanation:
In a triangle(3 sides), the total number of degrees is 180 degrees.
In a quadrilateral(4 sides), the total number of degrees is 360 degrees.
^^ Now convert this into a formula
Let's say s = number of sides
d = total degrees
s: d:
3 --> 180
4 --> 360
Hence, the relation between s and d is:
(s-2)*180
Let's test this relation:
3:
(3-2)*180 = ==> plugin 3 for s in (s-2)*180
1*180 = 180 √
4:
(4-2)*180 = ==> plugin 4 for s in (s-2)*180
2*180 = 360 √
Now apply this formula to an 8-sided figure:
s = 8
(s-2)*180 =
(8-2)*180 = ==> plugin 8 for s in (s-2)*180
6*180 = 1080 total degrees in the 8-sided figure
Since all 8 sides in the 8-sided figure are equal, all 8 angles are equal as well.
Hence, the measure of each angle is:
1080 / 8 = 135 degrees
Hence:
16x + 23 = 135 ==> solve for x
16x = 112 ==> subtract 23 on both sides to isolate x
x = 7 ==> divide both sides by 16 to isolate x