Question

6. ABCD is a kite and ZA = ZC. If ZCAD = 60° and ZCBD = 45°, find
(a) BCD
(b) CDA​

Answer 1

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Step 1 is to draw a picture and label it with the known angles and sides. Unfortunately, I can't draw one on this text editor. 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:

The diagonals intersect at right angles

Diagonal AC bisects diagonal BD

Diagonal AC bisects angles BAD and BCD

Given property 3 above, if angle CAD = 40o then angle BAC = 40o

Look at triangle BCE. Angle CBE is given as 60o and angle BEC = 90o (property 1 above).

Angle BCA (same as BCE) = 180o - (90o+60o) = 30o

By property 3, if angle BCA = 30o, then angle BCD = 60o

$\bold{\pink{\fbox{\blue{ 8♡+Follow = lB }}}}$