Let's solve the problem step by step.

Given:

• ∠A and ∠B are complementary angles. This means: $∠A + ∠B = 90^\circ$
• The measure of ∠A is 42 degrees more than 3 times the measure of ∠B.

Let:

• ∠B = $x$
• ∠A = $3x + 42$

Since the angles are complementary, we can set up the following equation:

$∠A + ∠B = 90^\circ$ Substitute the expressions for ∠A and ∠B: $(3x + 42) + x = 90$

Combine like terms:

$4x + 42 = 90$

Subtract 42 from both sides:

$4x = 48$

Divide both sides by 4:

$x = 12$

Thus, the measure of ∠B is 12 degrees.

The correct answer is:

• $∠B = 12^\circ$

Would you like further explanation on any of these steps, or do you have additional questions?

Here are 5 related questions for further practice:

1. If two angles are complementary, and one angle is 20 degrees less than twice the other, what are the measures of the angles?
2. What is the measure of each angle if two angles are complementary and one angle is three times the other?
3. Two angles are supplementary. One angle is 30 degrees more than twice the other. What are the measures of the angles?
4. How do you solve for an angle in a right triangle if you know one of the acute angles?
5. What are the steps to find the complement of a given angle?

Tip: When dealing with angle relationships, setting up an equation with variables and solving step by step is a powerful approach!