Question

In kite ABCD, mZBAE = 28º and mZBCE = 58°. Find mZABE.

B
E
А
С
D
mLABE =

Answer 1

m∠ABE = 62°

Explanation:

Since, the given quadrilateral is a kite, diagonals will intersect at 90°.

Therefore, m∠AEB = m∠CEB = 90°

m∠BAE = 28° [Given]

m∠BCE = 58° [Given]

From ΔABE,

m∠BAE + m∠BEA + m∠ABE = 180°

28° + 90° + m∠ABE = 180°

m∠ABE = 180° - 118°

= 62°

Therefore, measure of angle ABE = 62°.