We are given that ∠A and ∠B are complementary, meaning their measures add up to 90°. The problem gives the following information:

• $m\angle A = (4x + 1)^\circ$
• $m\angle B = 17^\circ$

Step 1: Set up the equation for complementary angles.

Since the angles are complementary: $m\angle A + m\angle B = 90^\circ$ Substituting the given values: $(4x + 1) + 17 = 90$

Step 2: Solve for $x$.

Simplify the equation: $4x + 1 + 17 = 90$ $4x + 18 = 90$ Subtract 18 from both sides: $4x = 72$ Divide both sides by 4: $x = 18$

Step 3: Find $m\angle A$.

Now that we have $x = 18$, substitute it into the expression for $m\angle A$: $m\angle A = 4(18) + 1 = 72 + 1 = 73^\circ$

Final Answer:

• $x = 18$
• $m\angle A = 73^\circ$

Would you like more details or have any other questions?

Here are some related questions to further explore:

1. How do we know when angles are complementary?
2. What is the difference between complementary and supplementary angles?
3. How would the problem change if the angles were supplementary?
4. What is the general formula for solving for $x$ in similar angle problems?
5. How can complementary angles appear in geometry problems?

Tip: Complementary angles always add up to 90°, while supplementary angles add up to 180°.