Find the measure of angle 𝐷.
First of all, we should consider what kind of quadrilateral 𝐴𝐵𝐶𝐷 is. We see that line segments 𝐴𝐷 and line segment 𝐵𝐶 are parallel, so we can write that down. We also see that line segment 𝐷𝐶 and line segment 𝐴𝐵 are parallel. Therefore, quadrilateral 𝐴𝐵𝐶𝐷 is a parallelogram.
And one property of parallelograms is that opposite angles are equal. In this quadrilateral, that means the measure of angle 𝐷 will be equal to the measure of angle 𝐵, and the measure of angle 𝐵 is 103 degrees.
By confirming that this shape is a parallelogram, we were able to see that the opposite angles are equal. And therefore, the measure of angle 𝐷 is 103 degrees.