Question

∠ A and ∠B are complementary. If m∠A=2x+23 and m∠B=4x−29, find the measure of ∠B.

Answer 1

Answer:

35°

Step-by-step explanation:

Complementary angles add up to 90°.

=> 2x+23+4x-29 = 90°

=> 6x-6 = 90°

=> 6x = 90+6

=> 6x = 96°

=> x = 16°

∠B = 64°-29° = 35°

Answer 2

If 2 angles are complementary, then it means they sum up to 90°

∠A + ∠B = 90°

⇒ (2x + 23)° + (4x - 29)° = 90°

⇒ 2x + 23 + 4x - 29 = 90°

⇒ 6x - 6 = 90°

⇒ 6x = 90° + 6

⇒ 6x = 96°

⇒ x = 96 ÷ 6

⇒ x = 16

Now, let us find the measure of ∠B

∠B

= (4x - 29)°

= 4(16) - 29

= 64 - 29

= 35°

∴ ∠B = 35°