Question

In △ABC,AB=AC. Points D and E are on the sides BC and AC respectively such that AD=AE. If ∠BAD=30∘, then the measure of ∠EDC is:

A. 10∘
B. 15∘
C. 20∘
D. 25∘

Answer 1

The measure of ∠EDC is 15°, determined by using the properties of isosceles triangles and the angle sum property of a triangle.

Step-by-step explanation:

The question asks to find the measure of ∠EDC in a triangle with specific properties. Since triangle ABC is isosceles with AB = AC and AD = AE, and ∠BAD is given as 30°, we can conclude that ∠BAE is also 30° because triangles ADE and ADB are isosceles as well. The angle sum property of triangle ABE gives us ∠AEB as 120°. Since AE = AD, triangle AED is isosceles and thus ∠ADE and ∠AED are 30° each. This further gives ∠DEC as 150° since ∠AED and ∠DEC make a straight line. Now, triangle CDE is isosceles with CD = CE, so the angles at the base are equal, meaning that ∠DCE is also 15°. Therefore, the measure of ∠EDC is 15°.