Question

In △ABC, the length of median BM is half the length of side AB and ∠ABM measures 40°. Find m∠ABC.

Answer 1

m∠ABC = 180.

Explanation:

In a triangle, the median to the side opposite the largest angle bisects that angle.

Since BM is a median, it bisects ∠C, the angle opposite side AB.

Let's call the angle opposite side AB angle x, so x/2 = 40.

Therefore, x = 80

Since a triangle has 180 degree, then if we add all the angles in the triangle we get:

m∠ABC = m∠BAC + m∠BCA + m∠CAB = x + (180-x) + (180-x) =180

So m∠ABC = 180