Final answer:
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