Answer:
∠ 1: 71°
∠ 2: 109°
∠ 3: 109°
Explanation:
The first angle I found was angle 3:
We can draw a straight line down through the middle of the trapezoid. That creates a quadrilateral for us, and since both the top and bottom lines were parallel, we have 3 angles already. The given angle is 71 and since we drew a perpendicular line through the middle of the parallel lines, the two angles of the perpendicular line are both 90 degrees.
The sum of all angles within a quadrilateral = 360 degrees
71° + 90° + 90° + ∠ 3 = 360°
∠ 3 = 360° - 90° - 90° - 71°
∠ 3 = 109°
Since the trapezoid is isosceles, opposite angles must be supplementary, meaning that they must add up to 180 degrees.
Angle 2
∠ 2 + 71° = 180°
∠ 2 = 109°
Angle 1
∠ 1 + 109° = 180°
∠ 1 = 71°