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Answer:

To find the measurement of angle ZBDC in rhombus ABCD, we need to use the properties of a rhombus.

In a rhombus:

1. All sides are congruent.

2. Opposite angles are congruent.

3. The diagonals bisect each other at right angles.

Given that ZDAB = 2x + 150° and ZDCB = 3x - 30°, we know that these are opposite angles in the rhombus. Therefore:

ZDAB = ZBCD

So, we can set up the equation:

2x + 150° = 3x - 30°

Now, let's solve for x:

2x - 3x = -30° - 150°

-x = -180°

Now, divide both sides by -1 to isolate x:

x = 180°

Now that we've found the value of x, we can find the measurement of angle ZBDC by plugging it into one of the angle expressions. Let's use ZDAB = 2x + 150°:

ZBDC = 2x + 150°

ZBDC = 2(180°) + 150°

ZBDC = 360° + 150°

ZBDC = 510°

However, angles in a rhombus cannot be greater than 180 degrees, so there seems to be an issue in the problem statement. A rhombus should have angles less than or equal to 180 degrees. None of the answer choices (a) 35°, (b) 45°, (c) 42°, or (d) 374° are correct for this situation.

Please double-check the problem statement or provide additional information if there's a mistake or missing context.

Step-by-step explanation:

Step-by-step explanation:

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