Question 1067882: The diagonals of rhombus ABCD intersect at E. Given that m∠BAC=53°, DE=8, and EC=6, find m∠DAC.
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
In any rhombus, diagonals bisect its angles.
See the lesson
Diagonals of a rhombus bisect its angles
in this site.
Therefore, m∠DAC = m∠BAC = 53°.
The rest of the condition ("DE=8, and EC=6") is irrelevant, unnecessary and excessive. It is not used in the solution.
Nevertheless, I checked if that unnecessary part is consistent with the core part of the condition (m∠BAC = 53°).
From DE=8, and EC=6 I got m∠BAC = 53.16 degrees.
Make the conclusion on your own.
Formally speaking, the condition is defective.
But the defect, although it does present, is not so big and, probably, is not fatal.
So, you do your conclusion.
Had I be at your place, I'd simply omitted this excessive part to avoid unnecessary complications.
---------------------
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part if this textbook under the topic "Properties of rhombis".
|
|
|
