Question

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

Explanation:

Step1: Use the linear - pair relationship

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

Step2: Simplify the left - hand side of the equation

Combine like terms: \(235+161-3x - x=180\), which is \(396-4x = 180\)

Step3: Solve for \(x\)

Subtract \(396\) from both sides: \(-4x=180 - 396=-216\)
Divide both sides by \(-4\): \(x = 54\)

Step4: Find \(m\angle2\)

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

Step5: Use the corresponding - angles relationship

Since the two lines are parallel, \(\angle A\) and \(\angle2\) are corresponding angles. So \(m\angle A=m\angle2\)

Answer:

\(107^{\circ}\)