Answer:

Step-by-step explanation:

We know that the sum of angles in a quadrilateral is 360 degrees.

So,

angle A + angle B + angle C + angle D = 360 degrees

We are given:

angle A = 3x + 2

angle B = (4x - 24)

angle C = (2x + 2)

angle D = x + 10

Substituting these values in the equation for the sum of angles, we get:

(3x + 2) + (4x - 24) + (2x + 2) + (x + 10) = 360

Simplifying and solving for x, we get:

10x - 10 = 360

10x = 370

x = 37

Now we can find the value of angle D:

angle D = x + 10 = 37 + 10 = 47 degrees

To find angle ADC, we need to subtract angle C from angle D:

angle ADC = angle D - angle C = 47 - (2x + 2) = 47 - (2(37) + 2) = 47 - 76 = -29

The measure of angle ADC is -29 degrees. However, this is not a possible angle measure since angles cannot be negative. This means that there is an error in the problem statement or in the calculations.

Step-by-step explanation:

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