Dear experts please explain why my answer is wrong for this question and also check the solution provided by you [ 2 different answers are given ] .....!!!!
Q12)
Use the following information to answer the next question.
The given figure shows two triangles ÎACD and ÎBCD of equal areas. BD is angle bisector of âABC
What is the measure of âBCE, if âABD = 35Â?
- A)
35Â
- B)
44Â
- C)
55Â
- D)
70Â
In the figure, it is seen that, ÎACD and ÎBCD are on the same base DC.
It is given that, area of ÎACD is equal to the area of ÎBCD.
We know that, two triangles having the same base (or equal bases) and equal areas lie between the same parallels.
ÎACD and ÎBCD lie between the same parallels.
As, DC is their common base, these two triangles lie between the same parallels DC and AB.
That is, DC||AB
â´âBCE = âABC
(Since they are pair of alternate interior angles, where BC is the transversal)
Given that, BD is the angle bisector of âABC.
â´âABC = 2âABD
= 2 Ã 35Â [âABD = 35Â (given)]
= 70Â
Thus, âBCE = âABC = 70Â
The correct answer is D.