Question

∠A and \angle B∠B are complementary angles. If m\angle A=(4x+24)^{\circ}∠A=(4x+24) ∘ and m\angle B=(3x-4)^{\circ}∠B=(3x−4) ∘ , then find the measure of \angle B∠B.

Answer 1

The measure of \angle B∠B is 26 degrees.

Since complementary angles have measures that add up to 90 degrees, we can set up the equation:

(4x+24)° + (3x-4)° = 90°

Combining like terms, we get:

7x + 20 = 90

Subtracting 20 from both sides, we get:

7x = 70

Dividing both sides by 7, we find the value of x:

x = 10

Substituting the value of x back into the expression for m\angle B∠B, we get:

m\angle B=(3x-4)° = (3(10)-4)° = 26°

Therefore, the measure of \angle B∠B is 26 degrees.

Answer 2

m∠B = 26°

Explanation:

∠A and ∠B being complementary means m∠A + m∠B = 90°

4x + 24 + 3x - 4 = 90

7x + 20 = 90

7x = 70

x = 10

m∠B = (3•10 - 4)° = 26°