BD is the diagonal of parallelogram ABCD such that ∠CBD = 12x, ∠ABD = 7y, ∠ADB…

When a transversal cuts two parallel lines, the alternate interior angles formed are equal. In a parallelogram, each diagonal acts as a transversal for both pairs of parallel (opposite) sides, so it splits the parallelogram's vertex angles into parts that pair up as alternate angles across the diagonal.

1. Since AD is parallel to BC and diagonal BD is the transversal, ∠ADB and ∠CBD are alternate interior angles, so ∠ADB = ∠CBD. This gives 60° = 12x, so x = 5.

2. Since AB is parallel to CD and diagonal BD is the transversal, ∠ABD and ∠CDB are alternate interior angles, so ∠ABD = ∠CDB. This gives 7y = 28°, so y = 4.

3. Substitute into the required expression: 2x + 3y = 2(5) + 3(4) = 10 + 12 = 22.

Cross-check: ∠ABC = ∠ABD + ∠DBC = 28° + 60° = 88°, and ∠ADC = ∠ADB + ∠BDC = 60° + 28° = 88°. Since ∠ABC = ∠ADC, the two opposite vertex angles B and D — which must be equal in any parallelogram — match, confirming that the values of x and y are consistent.

So 2x + 3y = 22°.