Question

∠A and ∠B are complementary angles. If m∠A=(6x+1) ∘ and m∠B=(8x-23) ∘, then find the measure of∠B.

Answer 1

Given that <A and <B are complementary angles, the measure of angle B is: $41^{\circ}$

Apply the knowledge of what complimentary angles are to solve for x then find the measure of <B.

Since <A and <B are both complimentary angles, therefore:

• <A + <B = 90 degrees.

• Given:

m<A = (6x+1)

m<B = (8x-23)

• Substitute

$(6x+1) + (8x-23) = 90$

• Open the bracket

$6x+1 + 8x-23 = 90$

• Add like terms

$6x+1 + 8x-23 = 90\\\\14x - 22 = 90$

• Add 22 to both sides

$14x = 90 + 22\\\\14x = 112$

• Divide both sides by 14

$x = 8$

• Find m<B by plugging in the value of x

$m \angle B = 8x-23\\\\m \angle B = 8(8) - 23\\\\m \angle B = 41^{\circ}$

Therefore, given that <A and <B are complementary angles, the measure of angle B is: $41^{\circ}$

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