Answer:
m∠BCA = 43°
Step-by-step explanation:
ABCD is a kite having m∠BAD = 46° and m∠ABC = 114°
∠BAD and ∠BCA are the vertex angles of the kite.
Since, diagonal of kite bisect the vertex angles
m∠BAC = m∠DAC = [tex]\frac{1}{2}(46^{\circ})[/tex]
m∠BAC = 23°
By applying triangle sum theorem in ΔABC,
m∠ABC + m∠BCA + m∠BAC = 180°
114° + m∠BCA + 23° = 180°
m∠BCA = 180° - (114° + 23°)
= 43°
