In a right-angled triangle, the difference between the measures of the two acute (non right) angles is 8°. What is the measure (in degrees) of the smallest angle of the triangle?

Introduction / Context:
This is a basic angle sum question for a right angled triangle. Every right angled triangle has one 90° angle and two acute angles. The problem gives the difference between those two acute angles and asks you to find the smaller one using simple algebra.

Given Data / Assumptions:

• The triangle is right angled, so one angle is 90°.
• Let the acute angles be θ and φ.
• The difference between the two smaller angles is 8°.
• We need the smallest angle of the triangle.

Concept / Approach:
In any triangle, the sum of the three interior angles is 180°. In a right triangle, one angle is 90°, so the other two must add up to 90°. Given their difference, you can set up a pair of linear equations and solve for the individual angles using basic algebraic techniques.

Step-by-Step Solution:
Step 1: Let the smaller acute angle be x degrees.Step 2: Then the larger acute angle is x + 8 degrees because their difference is 8°.Step 3: In a right triangle, sum of all angles is 180°. One angle is 90°, so x + (x + 8) + 90 = 180.Step 4: Simplify: 2x + 8 + 90 = 180, so 2x + 98 = 180.Step 5: Solve: 2x = 180 - 98 = 82, hence x = 41.Step 6: Therefore the smallest angle measures 41°.

Verification / Alternative check:
Check by computing the other acute angle: 41° + 8° = 49°. Now sum of angles is 90° (right angle) + 41° + 49° = 180°, which confirms the result is consistent.

Why Other Options Are Wrong:
37°, 42°, 49° and 35° do not satisfy both conditions of adding with another angle to 90° and having a difference of exactly 8°. Only 41° leads to a matching pair of 41° and 49° that works.

Common Pitfalls:
Students sometimes forget to include the right angle in the 180° sum or subtract the difference incorrectly. Carefully defining variables for the smaller and larger acute angles and writing the equation avoids confusion.

Final Answer:
The smallest angle of the triangle is 41°.