Answer:
x = 22°, y = 70°
Explanation:
Isosceles Triangles
The base angles of an isosceles triangle are those formed by the base and one leg of the triangle.
On the other side, the base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.
We are given an isosceles triangle with base angles 3x-11 and 2x+11. Applying the theorem as explained above:
3x - 11 = 2x + 11
Subtracting 2x:
x - 11 = 11
Adding 11:
x = 22
The base angles have a measure of
3x - 11 = 3*22 - 11 = 55°
Thus, the remaining angle of the triangle is:
y = 180° - 2*55° = 180° - 110° = 70°
x = 22°, y = 70°