Question

In triangle ABC angle A = 50 degree.BC is produced to point D .The bisectors angle ABC and angle ACD meet at E. Find angle E

Answer 1

By using the Angle Bisector Theorem on Triangle ABC and ADC, you can determine that the measure of the angle at point E in Triangle ABC where the bisectors of ∠ABC and ∠ACD intersect is 90 degrees.

Step-by-step explanation:

In Triangle ABC, with the bisectors of ∠ABC and ∠ACD intersecting at E, we are asked to find the measure of ∠E.

The angle bisector theorem states that the ratio of the lengths of the two segments created by the bisector of an angle in a triangle is equal to the ratios of the lengths of the opposite sides of the triangle. In the context of angle measures, if a line segment bisects an angle of a triangle, then it cuts the opposite side into two segments that are proportional to the other two sides.

Applying this theorem to triangle ABC and ADC, we have that:

∠ABC + ∠ACD = 180° (Because these angles are supplementary i.e. lie on a straight line).

Now ∠E = 1/2 * ( ∠ABC + ∠ACD)

Plugging values we get ∠E = 1/2 * (180°) = 90°

Learn more about Angle Bisector Theorem