A = 82 – 8° B = 5x + 25° Solve for x and then find the measure of B:

To solve for x, we can use the information given that A = 82 – 8° and B = 5x + 25°, assuming that A and B are angles that are either complementary or supplementary (since we’re not given any additional context, we’ll have to base our solution on this assumption).

If A and B are complementary, then A + B = 90°. If A and B are supplementary, then A + B = 180°.

Without additional information, we cannot know if they are complementary or supplementary. But let's handle both cases:

**Case 1: A and B are complementary (A + B = 90°)**

1. Plug in the values for A and B into the equation: (82 – 8°) + (5x + 25°) = 90°

2. Simplify and combine like terms: 82° – 8° + 5x + 25° = 90° 74° + 5x + 25° = 90° 99° + 5x = 90°

3. Subtract 99° from both sides: 5x = 90° - 99° 5x = -9°

4. Divide by 5 to solve for x: x = -9° / 5 x = -1.8°

Now to find B given that x is -1.8°:

B = 5x + 25° B = 5(-1.8°) + 25° B = -9° + 25° B = 16°

**Case 2: A and B are supplementary (A + B = 180°)**

1. Plug in the values for A and B into the equation: (82 - 8°) + (5x + 25°) = 180°

2. Simplify and combine like terms: 74° + 5x + 25° = 180° 99° + 5x = 180°

3. Subtract 99° from both sides: 5x = 180° - 99° 5x = 81°

4. Divide by 5 to solve for x: x = 81° / 5 x = 16.2°

Now to find B given that x is 16.2°:

B = 5x + 25° B = 5(16.2°) + 25° B = 81° + 25° B = 106°

Without additional information, we can't definitively determine the value of x or B. It's also possible that A and B have some other relationship not addressed here. For the most accurate solution, more context from the problem would be needed.