There are a lot of problems here. I'll do the first three (problems 2, 3, 6) to get you started. If you're still stumped, then make a new post for the remainder of the problems.

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Problem 2

**Angle 2 is 75 degrees** because 75 + 105 = 180. Or put another way, 180 - 105 = 75. Angle 1 and angle 2 add to 180 degrees as they form a straight angle. They are considered supplementary angles.

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Problem 3

a) A rhombus with no right angles is one example of a parallelogram that isn't a rectangle

b) A square must have all four sides the same length, whereas a rectangle can have 2 pairs of sides that are different such as a 7 by 8 rectangle.

c) It is possible to have a parallelogram with two sets of different opposite sides, which means that not all four sides are the same length, so it wouldn't be a rhombus. This is similar to part b above, except that the angles don't all have to be 90

d) A parallelogram is a quadrilateral with opposite pairs of parallel sides

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Problem 6

Check out the attached image to see the drawing for problem 6.

As the diagram shows, RT is one of the diagonals. The other diagonal cuts RT in half at point A. This means segment RA is exactly half that of RT. Or RT is twice that of RA

2*RA = RT

2*(2x+3) = x+15

4x+6 = x+15

4x-x = 15-6

3x = 9

x = 3

If x = 3, then RT = x+15 = 3+15 = 18. So RT is 18 units long.