DS2011

Hmm... I see that we already have all we need to find the area, WX and XY. we just multiply 2 by 3 and get 6.

Answer: 6

I am trying to draw quadrilateral BCED but am failing to get the given lengths of the side to make sense. I don't know how to draw the quadrilateral. If you could upload an image of it, and where points B, C, E, D, and A are that would help a lot.

I haven't really learned this stuff at school, but I can assume that if AB and CD are parallel and chord AC is 100, then chord BD must also be 100, so that makes the measure of angle BOD = 100°

Answer: 100°

If the question  asks the sum of all possible values, maybe there are more than 1, but the only one that is right for me is 5/2.

Answer: 5/2 yes

By the Alternate Interior Angles Theorem, angle HDF and angle F are congruent, so angle F = 30 degrees.

By the Triangle Angle Sum Theorem, 55 + 30 + angle E = 180

E = 180 - 55 - 30 = 95 degrees

Answer: 95 degrees

 just wanted to show the work using the theorems if you needed it.

I think I know what you are saying, and that is Extending GH and then the vertical angle is 80 degrees, but I am not sure where 40 degrees came from. If you tried 180 - 80, you would get 100. Also, note that GH and CD would not be parallel to each other.

Actually, when finding that angle E is 60 degrees, you could use the Alternate Interior Angles Theorem that states that the two angles that are alternate interior angles are congruent to find that 60° ≅ x, so x = 60 degrees

Skipped 1 step this way.

By Triangle Angle Sum Theorem, the interior angle E is 180 - 40 - 80 = 60 degrees.

The angle adjacent to angle E is 180 - 60 = 120 degrees

By the Same-Side Interior Angles Postulate, 120 + x = 180 since they are supplementary to each other

x = 60 degrees

Answer = 60°