Question

three angles are shown, ∠bwx, ∠cwx, and ∠bwc. if ( mangle bwx = (5.5x + 2.9)^circ ), ( mangle cwx = (3.5x - 10.7)^circ ), and ( mangle bwc = 102^circ ), what is ( mangle cwx )?
options: ( 22^circ ), ( 32^circ ), ( 70^circ ), ( 80^circ )

Explanation:

Step1: Set up the angle addition equation

From the diagram, we know that \( m\angle BWC = m\angle BWX + m\angle CWX \). Substituting the given expressions, we get:
\( 102=(5.5x + 2.9)+(3.5x - 10.7) \)

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms:
\( 102=(5.5x+3.5x)+(2.9 - 10.7) \)
\( 102 = 9x-7.8 \)

Step3: Solve for \( x \)

Add \( 7.8 \) to both sides:
\( 102 + 7.8=9x \)
\( 109.8 = 9x \)
Divide both sides by \( 9 \):
\( x=\frac{109.8}{9}=12.2 \)

Step4: Find \( m\angle CWX \)

Substitute \( x = 12.2 \) into the expression for \( m\angle CWX \):
\( m\angle CWX=(3.5\times12.2-10.7)^\circ \)
First, calculate \( 3.5\times12.2 = 42.7 \)
Then, \( 42.7-10.7 = 32 \)
So, \( m\angle CWX = 32^\circ \)

Answer:

\( 32^\circ \) (corresponding to the option with \( 32^\circ \))