A triangle has 3 angles. Here you are mentioning two pairs of angles, which is four angles.
Then I believe that the figure may be an isosceles trapezoid, instead of a triangle.
The trapezoid is a quadrilateral.
In an isosceles trapezoid there are two pair of equal base angles. Call the angles x, x, y and y.
The internal angles of a quadrilateral sum 360 degrees, then 2x + 2y = 360.
Given that the measure of one pair is twice the measure of the other, you can state that 2y = 4x and 2x + 4x = 360
Now solve the equation:
6x = 360
x = 360 / 6
x = 60.
Then the measures are 60, 60, 120 and 120 degrees.
