Question

two bisectors In A ABC, ZA= 50° and BC is produced to a point D. The bisectors of 2. ABC and 2 ACD- at E. Find ZE In A ABC, 2 B = 60°, ZC = 40°, ALI BC and AD bisects 2.

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Answer 1

Answer:

In the given triangle, ∠ACD = ∠A + ∠B. (Exterior angle is equal to the sum of two opposite interior angles.) We know that the sum of all three angles of a triangle is 180°. Therefore, for the given triangle, we know that the sum of the angles = 180° ∠ABC + ∠BCA + ∠CAB = 180° ∠A + ∠B + ∠BCA = 180° ∠BCA = 180° – (∠A + ∠B) But we know that EC bisects ∠ACD Therefore ∠ECA = ∠ACD/2 ∠ECA = (∠A + ∠B)/2 [∠ACD = (∠A + ∠B)] But EB bisects ∠ABC ∠EBC = ∠ABC/2 = ∠B/2 ∠EBC = ∠ECA + ∠BCA ∠EBC = (∠A + ∠B)/2 + 180° – (∠A + ∠B)Read more on Sarthaks.com - https://www.sarthaks.com/687772/in-abc-a-50and-bc-is-produced-to-a-point-d-the-bisectors-of-abcand-acd-meet-at-e-find-e