Question

current skill
find the measure of angle 4.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. Angle \(2\) and the \(71^{\circ}\) angle are vertical angles. So, \(\angle2 = 71^{\circ}\).

Step2: Use linear - pair relationship

\(\angle2\) and \(\angle4\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So, \(\angle2+\angle4 = 180^{\circ}\).

Step3: Solve for \(\angle4\)

Substitute \(\angle2 = 71^{\circ}\) into \(\angle2+\angle4 = 180^{\circ}\). Then \(\angle4=180^{\circ}-\angle2\).

$$ \angle4 = 180^{\circ}- 71^{\circ}=109^{\circ} $$

Answer:

\(109^{\circ}\)