Question

A
E
B
(4) In the figure nearby, chord AC and chord DE
intersect each other in point B.
i. If m(arc AE) = 50, m( arc DC) =
= 140,
then < DBC = ? _ ABD = ?
ii. If m(arc AD)
70, m_ EBC = 50, then
m(arc EC) = ?

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Answer 1

Answer:

Chords AC and DE intersect internally at point B. ∴ ∠ABE = 1/2 [m(arc AE) + m(arc DC)] ∴ 108° = 1/2 [95° + m(arc DC)] ∴ 108° × 2 = 95° + m(arc DC) ∴ 95° + m(arc DC) = 216° ∴ m(arc DC) = 216° – 95° ∴ m(arc DC) = 121°Read more on Sarthaks.com - https://www.sarthaks.com/851631/in-the-adjoining-figure-chords-ac-and-de-intersect-at-b-if-abe-108-m-arc-ae-95-find-m-arc-dc