Question

if ( x = 67^{circ} ), find the measures of angles 1, 2, and 3.
( mangle1=square^{circ} )

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Angle \(x\) and \(\angle2\) are vertical angles. So \(m\angle2 = x=67^{\circ}\)

Step2: Use the property of linear - pair angles

\(x\) and \(\angle1\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So \(m\angle1=180 - x\)
Substitute \(x = 67^{\circ}\), then \(m\angle1=180-67 = 113^{\circ}\)

Step3: Use the property of vertical angles again

\(\angle1\) and \(\angle3\) are vertical angles. So \(m\angle3=m\angle1 = 113^{\circ}\)

Answer:

\(m\angle1 = 113^{\circ}\), \(m\angle2=67^{\circ}\), \(m\angle3 = 113^{\circ}\)