SOLUTION: Draw a kite ABCD ,AB=AD,BC=CD;CAD=40 AND CBD=60 CALULATE A)BAC B)BCA c)ADC PLEASE I NEED WITH EXPLANTION

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Question 1111121: Draw a kite ABCD ,AB=AD,BC=CD;CAD=40 AND CBD=60
CALULATE
A)BAC
B)BCA
c)ADC
PLEASE I NEED WITH EXPLANTION
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

draw a picture and label it with the known angles and sides
be sure to draw in the two diagonals, AC and BD
label the point where the diagonals cross as point E
In a kite, there are three important properties you need to know to solve this problem:
1. The diagonals intersect at right angles
2. Diagonal AC bisects diagonal BD
3. Diagonal AC bisects angles BAD and BCD
Given property 3 above, if angle CAD+=+40° then angle BAC+=+40°

Look at triangle BCE. Angle CBE is given as 60° and angle BEC+=+90° (property 1 above).
Angle BCA+%28same_+as_+BCE%29+=+180++-+%2890+%2B60+%29+=+30°

By property 3, if angle BCA+=+30° , then angle BCD+=+60°
answer:
A)BAC+=+40°
B)BCA=+30°
c)BCD+=+60°