Question

if ( mangle1=(235 - 3x)^{circ} ) and ( mangle2=(161 - x)^{circ} ), what is ( mangle a? ) ( mangle a=)____

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(235 - 3x)^{\circ}\) and \(m\angle2=(161 - x)^{\circ}\) into the equation:
\((235 - 3x)+(161 - x)=180\)

Step2: Simplify the equation

Combine like - terms:
\(235+161-3x - x=180\)
\(396-4x = 180\)
Subtract 396 from both sides:
\(-4x=180 - 396\)
\(-4x=-216\)
Divide both sides by - 4:
\(x = 54\)

Step3: Find \(m\angle2\)

Substitute \(x = 54\) into \(m\angle2=(161 - x)^{\circ}\)
\(m\angle2=(161-54)^{\circ}=107^{\circ}\)

Step4: Use the property of corresponding angles

Assume \(\angle A\) and \(\angle2\) are corresponding angles (assuming parallel lines in the figure). Then \(m\angle A=m\angle2\)

Answer:

\(107^{\circ}\)