Question

1. find the measure of this angle. type a response

Explanation:

Step1: Use the concept of linear pairs

Angles in a linear pair sum to \(180^{\circ}\). The given angle \(72^{\circ}\) and angle \(1\) form a linear pair. So, \(\angle1 + 72^{\circ}=180^{\circ}\).

Step2: Solve for \(\angle1\)

\(\angle1=180^{\circ}- 72^{\circ}=108^{\circ}\)

Step3: Use the property of vertical angles

Vertical angles are equal. Angle \(3\) and the \(72^{\circ}\) angle are vertical angles. So, \(\angle3 = 72^{\circ}\)

Step4: Use the linear - pair property again for \(\angle2\)

\(\angle2+72^{\circ}=180^{\circ}\) (since \(\angle2\) and the \(72^{\circ}\) angle form a linear pair). So, \(\angle2 = 180^{\circ}-72^{\circ}=108^{\circ}\)

Assuming the question is asking for \(\angle1\) (as no specific angle number is mentioned in the problem statement, but if we consider the most common case where the non - given non - vertical angle adjacent to \(72^{\circ}\) is asked).

Answer:

\(108^{\circ}\)