Question

Find the measure of the missing angle in the kite , given kite ADCB with m < BAD = 46 degree and m < ABC = 114 degree find m

Answer 1

m∠BCA = 43°

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 =
`(1)/(2)(46^(\circ))`

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°