Question

In a triangle ABC, the measure of angle C is 90°. If angle A and angle B are complementary and the measure of angle A is 30 less than twice the measure of angle B, what is the measure of angle A?

A. 40
B. 45
C. 50
D. 55
E. 60

Answer 1

The measure of angle A in the right-angled triangle is 50°, which is found by expressing angle A as 2x - 30, where x represents the measure of angle B, and solving the equation formed by the fact that angles A and B are complementary to 90°.

Step-by-step explanation:

To find the measure of angle A in a right-angled triangle ABC, where angle C is 90°, and angles A and B are complementary, we use the information that the measure of angle A is 30 less than twice the measure of angle B. This is a classic example of an algebra problem involving angles in a triangle.

Let's denote the measure of angle B as x. Since angle A and angle B are complementary and the triangle is right-angled, we know that:

angle A + angle B = 90°

Given angle A is 30 less than twice angle B, we can write:

angle A = 2x - 30

We also have:

x + (2x - 30) = 90°

Combining the like terms gives us:

3x - 30 = 90

Adding 30 to both sides gives us:

3x = 120

Dividing both sides by 3 gives us:

x = 40

So, angle B is 40°. Now, we find angle A by plugging the value of x back into the expression for angle A:

angle A = 2(40) - 30

angle A = 80 - 30

angle A = 50°

Therefore, the measure of angle A is 50°, which corresponds to choice C in the question.