Question

Please help with geometry!

Answer 1

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