Question

If angles ∠A and ∠B are complementary, and ( m_A = (x – 23)^∘ ) and ( m_B = (2x + 29)^∘ , find the measure of ∠B .

a) ( x + 6 )
b) ( x - 6 )
c) ( 2x - 6 )
d) ( 3x + 6 )

Answer 1

To find the measure of ∠B when ∠A and ∠B are complementary, set up an equation with their given expressions, solve for x, and substitute back to get the measure of ∠B, which is 85 degrees.

Step-by-step explanation:

If angles ∠A and ∠B are complementary angles, it means that the sum of their measures is 90 degrees. Given ( m_A = (x – 23)^{°} ) and ( m_B = (2x + 29)^{°} ), we can set up an equation to find the value of x:

m_A + m_B = 90^{°}

(x – 23)^{°} + (2x + 29)^{°} = 90^{°}

Combine like terms:

3x + 6 = 90

Subtract 6 from both sides:

3x = 84

Divide by 3:

x = 28

Now, substitute x back into the equation for m_B to find the measure of ∠B:

m_B = (2(28) + 29)^{°}

m_B = (56 + 29)^{°}

m_B = 85^{°}

Therefore, the measure of ∠B is 85 degrees.