Question

if ( x = 67^{circ} ), find the measures of angles 1, 2, and 3.
( mangle 1 = 113^{circ} )
( mangle 2 = 67^{circ} )
( mangle 3 = )( ^{circ} )

Explanation:

Step1: Use the property of vertical angles

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

Step2: Use the property of supplementary angles

\(\angle1\) and \(x\) are supplementary (\(\angle1 + x=180^{\circ}\)). Given \(x = 67^{\circ}\), then \(m\angle1=180^{\circ}-67^{\circ}=113^{\circ}\).

Step3: Use the property of vertical angles again

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

Answer:

\(m\angle3 = 113^{\circ}\)