(d)If =m∠ABD30°, and point C is in the interior of ∠ABD, then =m∠ABC18° and =m∠CBD12°.=Counterexample:m∠ABC=, °m∠CBD°

It seems like there's some confusion in your question. However, I'll try to interpret it as best as I can.

Given:

1. m∠ABD = 30° (The measure of angle ABD is 30 degrees)
2. Point C is in the interior of ∠ABD (This means that angle ABD is split into two angles, ∠ABC and ∠CBD, by point C)

You're suggesting that:

1. m∠ABC = 18° (The measure of angle ABC is 18 degrees)
2. m∠CBD = 12° (The measure of angle CBD is 12 degrees)

However, for your suggestion to be correct, the sum of m∠ABC and m∠CBD should equal m∠ABD, since point C splits ∠ABD into ∠ABC and ∠CBD.

So, m∠ABC + m∠CBD = m∠ABD 18° + 12° = 30° 30° = 30°

So, your suggestion is correct. If m∠ABC is 18° and m∠CBD is 12°, then they would add up to m∠ABD, which is 30°.

If you're looking for a counterexample, you would need to find values for m∠ABC and m∠CBD that do not add up to 30°. For example, if m∠ABC was 20° and m∠CBD was 15°, then they would add up to 35°, not 30°, providing a counterexample.