a base angle of an isosceles triangle is 57 degrees. what is the measure of the vertex angle?

Question

i need to find the exact measurement of each side of the triangle

Answer 1

Please remember that the two base angles of an isosceles triangle are congruent. If one base angle measures 57 degrees, then so does the other one. If we sum these we obtain 114 degrees. Now, please recall that the sum of the three angles of any triangle is always 180 degrees. so the vertex angle here is found by 180 - 114 = 66. The vertex angle must measure 66 degrees. A far as the exact measurement of each SIDE of the triangle, that can not be determined form this information, only the size of each ANGLE. If we have the length of any one side, then we could use the law of sines to calculate the length of each side.