SOLUTION: Hi, Could someone help me on these problems please? Thank you! 1. A convex 14-gon has six interior angles that each measure 164 degrees. If the remaining interior angles are congr

Question 78899: Hi, Could someone help me on these problems please? Thank you!
1. A convex 14-gon has six interior angles that each measure 164 degrees. If the remaining interior angles are congruent, what is the measure of each remaining angle?
2. Polygon OPQRSTUVWXYZ is a regular dodecagon. If line QR and XY intersect at point J, find measure angle QJK.

Answer by mathdoc314(58) (Show Source): You can put this solution on YOUR website!
1.
The exterior angles add up to 360 total.
This is a convex 14-gon.
If six of the interior angles each meausre 164 degrees and the remaining ones are congruent then:
8 x + 6 * (180-164) = 360
8 x + 6 * 16 = 360
8x + 96 = 360
8x = 264
x = 264 / 8 = 33 degrees
The remaining interior angles measure (180-33) degrees which is 157
It is a miracle for sure
2. This is pretty funny. The main problem is in counting the letters
QR to RS: 1
RS to ST: 2
ST to TU: 3
TU to UV: 4
UV to VW: 5
VW to WX: 6
WX to XY: 7
There are only 12 sides on this thing so I have gone around more than halfway. The right number to use for the number of angles turned is 5
The angles are all the same measure going from one side to another in going around this regular dodecahedron (12 sides) and they measure 360/12 degrees which is 30 degrees on each turn
The answer, I think, is 30 degrees * 5 turns which is 150 degrees
You may want to draw a diagram to see if this is reasonable.

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