Hey, I have a geometry exam tomorrow and I'm trying to complete a review packet from my teacher. I was doing fine until I reached the section on rhombi. I can't out for the life of me how to do this problem. Could you please help me? Please provide an explanation, if you can, as well. I've attached a general reproduction of the original diagram.
If m<EBC = 132.6, find m<EBD.
The answer is 66.3. I know that it sounds simple just to divide the angle in half, but, that is how you do it.
Some proof would be this;
Given: In rhombus CDBE, <EBC = 132.6.
Prove: <DBE = 66.3
(Proof by contradiction)
Suppose m<DBE does not = 66.3. The measure of DEB is 47.4 due to the fact that the angles of a rhombus are supplementary. 132.6 + 47.4 does = 180, which proves that they are supplementary. If you made triangle DBE, then you would have to have the angle measures equal 180 in that triangle. One of the angles is 47.4, and the other two angles are congruent. If you subtract 47.4 from 180, you get 132.6, divide that by two and get 66.3. Therefore, the angles must be 66.3, as that are the only angles that fit.
Hope this helped a lot! Good luck on the test! Just had the second day of mine, and hopped on to ask a question of my own, but thought I should learn something by answering a few other questions.