Question

In a ΔABC, if point D is on the BC such that AB/AC=BD/DC and ∠B=70∘,∠C=50∘.
Find ∠BAD.

Answer 1

In triangle ABC, point D is on the side BC such that the ratio of AB to AC is equal to the ratio of BD to CD. To find the measure of angle BAD, we can use the fact that BD and DC are equal in length. By considering the triangle BDA as being isosceles, we can calculate that the measure of angle BAD is 60 degrees.

Step-by-step explanation:

In triangle ABC, point D is on the side BC such that the ratio of AB to AC is equal to the ratio of BD to CD. We need to find the measure of angle BAD.

1. Using the given information, we can set up the equation AB/AC = BD/CD.
2. Substituting the given values, we have AB/AC = BD/DC.
3. Since AB/AC can be simplified to 1/BD/DC, we can deduce that BD/DC = 1.
4. This means that BD and DC are equal in length, or BD = DC.
5. In triangle BDA, we have BD = DC, and angle BDA is common to both triangles BDA and CDA.
6. Therefore, triangle BDA is an isosceles triangle, and the measure of angle BAD is equal to the measure of angle BDA.
7. Since triangle BDA is isosceles, the measure of angle BDA can be found by subtracting the sum of angles B and C from 180 degrees, which is the sum of angles in a triangle.
8. Therefore, angle BAD = angle BDA = 180 - angle B - angle C.
9. Substituting the given values, we have angle BAD = 180 - 70 - 50 = 60 degrees.