Find the measure of angle 𝐶𝐵𝐷.
The first thing we can do is identify which angle 𝐶𝐵𝐷 is. Angle 𝐶𝐵𝐷 is here. From there, we need to think about what we can say about this shape. Since this quadrilateral has two pairs of parallel sides, we can say that 𝐴𝐵𝐶𝐷 is a parallelogram. And based on the properties of parallelograms, we know that in a parallelogram adjacent angles sum to 180 degrees, which means that angle 𝐴𝐵𝐶 and angle 𝐷𝐶𝐵 must add up to 180 degrees.
We know the measure of angle 𝐷𝐶𝐵 is 59 degrees. And then we can divide up angle 𝐴𝐵𝐶 into two smaller angles, one is angle 𝐴𝐵𝐷, which is 44 degrees, and the other angle is our missing angle, angle 𝐶𝐵𝐷, which means we can solve this equation for our missing angle. 44 plus 59 is 103 degrees. And that means to find the measure of angle 𝐶𝐵𝐷, we can subtract 103 degrees from both sides of the equation. And we see that our missing angle must measure 77 degrees.