Question

lines a and b are parallel lines cut by transversal f. if ( mangle1 = 110^{circ} ), what is ( mangle4 )?

Explanation:

Step1: Find the measure of the adjacent angle to ∠1

Since ∠1 and its adjacent angle form a linear - pair (sum to \(180^{\circ}\)). Let the adjacent angle be \(x\). Then \(x + m\angle1=180^{\circ}\). Given \(m\angle1 = 110^{\circ}\), we have \(x=180^{\circ}-110^{\circ}=70^{\circ}\).

Step2: Use the property of vertical angles

The angle \(x\) (which is \(70^{\circ}\)) and ∠4 are vertical angles. Vertical angles are equal. So \(m\angle4=x\).

Answer:

\(70^{\circ}\) (the second option)