The angle at the base of an isosceles triangle is 49 degrees 25 minutes. Find the angle at the vertex.

An isosceles triangle is a triangle in which the sides are equal and the angles between the base and the side are equal.

We also know the theorem that the sum of all three angles of a triangle is 180 degrees.
Thus, if we consider an isosceles triangle with angles ABC, where A, B are the angles at the base, and angle C is the angle at the apex, we get that A = B = 45 degrees 25 minutes.

And based on the theorem of the sum of the angles of a triangle, we get A + B + C = 180 degrees.
Then C = 180- (A + B).
Let’s plug in our values ​​and get the following answer:

C = 180 gr – (49 gr 25 min + 49 gr 25 min) = 180 gr – 98 gr 50 min = 81 gr 10 min.
(There are 60 minutes in one degree.)

Answer: The apex angle is 81 degrees 10 minutes.