Answers:
- For problem 3, the solution is x = 105
- For problem 4, the solution is x = 75
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Explanation for problem 3
For any convex polygon, the sum of the interior angles is equal to 180(n-2), where n is the number of sides.
In this case, we have a hexagon with 6 sides, so n = 6
The interior angles for the hexagon add to 180(n-2) = 180(6-2) = 720
We'll add the given angles and set that sum equal to 720, then solve for x.
135+110+125+120+125+x = 720
615+x = 720
x = 720-615
x = 105
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Explanation for problem 4
We'll use the same formula and idea as the previous problem.
This time we have n = 4 sides. This is a quadrilateral.
The interior angles add to 180(n-2) = 180*(4-2) = 360 degrees
So,
x+90+80+115 = 360
x+285 = 360
x = 360-285
x = 75
Note: the square angle marker represents 90 degrees