HarveyKlaus wrote:

Attachment:

3-09-16 10-12-26 AM.jpg

In triangle ABC, the measure of angle B is 80 as shown in the figure above. What is the measure of angle A?

1. Side AB and BC are the same length

2. The length of side AC is 10 inches.

The original answer is A but Im confused.

According to St1. we just know that the triangle is isosceles. So two angles are going to be equal. Since angle A is 80, we are left with 2 possibilities. The other two angles can be 50 50, or 80 20. In case its 50 50 then we the measure of the angle A is 50. But if its 80 20, we still will have the isosceles properties of the triangle as two angles with 80 and one 20.

Since, there could be two possible answer for angle A, I marked st1 as insufficient. But thats not the correct answer.

Where am I wrong?

Thanks for your comments!

Follow posting guidelines (link in my signatures), espcially putting all your analyses under spoilers, adding the OA and selecting the correct tag. This can not be an algebra question!!Your analysis of statement 1 is NOT correct. When you have an iscosceles triangle,

the angles opposite the equal sides are equal as well and vice versa.

Thus, if you are told that AB=BC ---> \(\angle {BAC} = \angle {BCA}\) and as in a triangle, sum of all the angles = 180 ---> \(\angle {BAC} = \angle {BCA} = 50\)

You can not have 80, 80, 20 as you are not told that AC = AB or AC=BC, you are in fact told that AB = BC. This is the reason why statement 1 is NOT sufficient.

As for statement 2, you can not have 1 unique triangle by giving you measure of 1 angle and the side opposite to this angle. You need atleast 2 angles and 1 side to completely define a triangle. Thus this statement is not sufficient.

A is thus the correct answer.

Hope this helps.