If     A and     B form a linear pair, and m     A = (x - 21)°, and m     B = (x + 15)°, then find x.

Sure, here are the steps to solve the problem:

1. Since A and B form a linear pair, the sum of their measures is 180°. This is because a linear pair of angles are adjacent angles whose non-common sides are opposite rays, which means they form a straight line and hence sum up to 180°.

2. So, we can set up the equation: m A + m B = 180°

3. Substituting the given values into the equation, we get: (x - 21)° + (x + 15)° = 180°

4. Simplifying the equation, we combine like terms to get: 2x - 6 = 180

5. Adding 6 to both sides of the equation to isolate the term with x, we get: 2x = 186

6. Finally, divide both sides of the equation by 2 to solve for x: x = 93

So, the value of x that satisfies the given conditions is 93.