Question

3 - 2: technology_mixed review_p8 (lms graded)
part 6 of 7
in the figure, m is parallel to n and ( mangle4 = 122^{circ} ). find the measures of the other angles.
( mangle6 = 122^{circ} )
( mangle2 = 122^{circ} )
( mangle8 = 122^{circ} )
( mangle5 = 58^{circ} )
( mangle3 = 58^{circ} )
( mangle7 = square^{circ} )

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle2 = m\angle4=122^{\circ}\)

Step2: Linear - pair angles

Since \(\angle2\) and \(\angle7\) form a linear - pair (\(\angle2+\angle7 = 180^{\circ}\)), then \(m\angle7=180 - 122=58^{\circ}\)

Step3: Corresponding angles

Since \(m\parallel n\), \(\angle2\) and \(\angle6\) are alternate - interior angles (\(m\angle2=m\angle6 = 122^{\circ}\)), \(\angle7\) and \(\angle3\) are alternate - interior angles (\(m\angle7=m\angle3 = 58^{\circ}\)), \(\angle5\) and \(\angle7\) are vertical angles (\(m\angle5=m\angle7 = 58^{\circ}\)), \(\angle8\) and \(\angle2\) are corresponding angles (\(m\angle8=m\angle2 = 122^{\circ}\))

Answer:

\(m\angle2 = 122^{\circ}\), \(m\angle3 = 58^{\circ}\), \(m\angle5 = 58^{\circ}\), \(m\angle6 = 122^{\circ}\), \(m\angle7 = 58^{\circ}\), \(m\angle8 = 122^{\circ}\)