Question

In the figure chord Ac and De intersect at B . If m(arc DC) =110, m (arc AE) = 94°, Find angle ABE
​

Answer 1

Given : chords AC and DE intersect at B  

m(arc DC) =110, m(arc AE) =94°  

To Find : ∠ABE

Solution:

∠ABE = ∠BCE + ∠BEC  ( exterior angle of triangle = Sum of opposite interior angle )

∠BCE = ∠ACE   as B lies on AC

∠ACE  = (1/2) m(arc AE)

=> ∠ACE  =  (1/2) 94°

= > ∠ACE  =47°

= >  ∠BCE = 47°

∠BEC  = ∠DEC  as B lies on DE

∠DEC =   (1/2) m(arc DC)

=> ∠DEC =     (1/2) 110°

=> ∠DEC =     55°

=> ∠BEC  = 55°

∠ABE = ∠BCE + ∠BEC

=> ∠ABE = 47°  + 55°

=> ∠ABE = 102°

Learn More

P is the centre of a circle. Chord MN = chord ML. Also, PQ is ...

https://brainly.in/question/13352182

Find the length of the chord AC where AB and CD are the two ...

https://brainly.in/question/6652737