Answer:
To solve this problem, let's use the properties of a right-angled triangle:
In a right-angled triangle, one of the angles is always 90°.
The sum of the angles in any triangle is always 180°.
In a right-angled triangle, the other two angles besides the right angle are always complementary, meaning they add up to 90°.
Given:
Triangle ABC is a right-angled triangle.
m∠C = 90° (the right angle)
Let's solve:
As the sum of angles in a triangle is 180°, and we know one angle is 90°, we can find the sum of the other two angles:
180° - 90° = 90°
We know that ∠A and ∠B are complementary, so:
m∠A + m∠B = 90°
As the question is asking for m∠B, we can deduce that m∠A must be one of the given options, and m∠B will be its complement.
Let's check each option:
A) If m∠A = 40°, then m∠B = 90° - 40° = 50°. Not in the options.
B) If m∠A = 45°, then m∠B = 90° - 45° = 45°. Option B is correct.
C) If m∠A = 60°, then m∠B = 90° - 60° = 30°. Option D matches, but B was already correct.
D) If m∠A = 30°, then m∠B = 90° - 30° = 60°. Option C matches, but B was already correct.
Therefore, the correct answer is B) 45°.