Anonymous

# I know the answer to this angle problem...but I don't get why!?

The question: The masure of angle AEC = 2x+7, and the measure of angle BEC = 5x-2. Find measure of angle DEB and FED.

measure of angle DEB=57

measure pf angle FED = 33

WHY!?!?!?!?

Relevance

I'm not sure there's enough information here. Are any of the angles complementary or supplementary? Are points A and B on a line segment, where EC is a line segment projecting from it (I'm assuming)?

If angles AEC and BEC are supplementary (sum equal to 180 degrees), then x = 25 degrees, but that doesn't tell us anything about points D and F, and we need that information as well.

AEC = 2x + 7

BEC = 5x - 2

AEC + BEC = 180 (*if* they're supplementary)

(2x + 7) + (5x - 2) = 180

7x + 5 = 180

7x = 175

x = 25

I'm guessing line segment DC intersects line segment AB at point E -- if x = 25 (from my assumption of the supplementary angles), then DEB is thus a congruent angle to AEC, explaining why it's 57 degrees. Consequently, if FED is formed as a complementary angle (sum of 90 degrees) to DEB, then that's why it's 33 degrees.

These are only guesses, though I'm only assuming I have the correct picture in my head. I hope that helps.