Question

In the given figure, A, B, C and D are four points on

a circle. AC and BD intersect at a point E such that

∠AED = 138° and ∠BAE = 75°. Find ∠ECD.​

Answer 1

Step-by-step explanation:

angle BAE = angle EDC = 75° [ angles in the same segment BC are equal ]

angle AED + angle DEC = 180° [ Linear pair]

angle DEC = 180° - 138° = 42°

In triangle EDC,

angle DEC + angle EDC + angle ECD = 180°

[ angle sum property of a triangle ]

angle ECD = 63°