Question

geometry hon - garcia (lms)
3 - 2: technology_mixed review_p8 (lms graded)
part 7 of 7
in the figure, ( m ) is parallel to ( n ) and ( m angle 4 = 122 ^ { circ } ). find the measures of the other
angles.
( m angle 6 = 122 ^ { circ } )( m angle 2 = 122 ^ { circ } )( m angle 8 = 122 ^ { circ } )( m angle 5 = 58 ^ { circ } )( m angle 3 = 58 ^ { circ } )( m angle 7 = 58 ^ { circ } )( m angle 1 = square ^ { circ } )

Explanation:

Step1: Use linear - pair relationship

Since \(m\) is parallel to \(n\) and we consider the linear - pair of \(\angle4\). \(\angle1\) and \(\angle4\) are supplementary (linear - pair of angles). If \(m\angle4 = 122^{\circ}\), then \(m\angle1=180^{\circ}-m\angle4\).

Step2: Calculate the measure of \(\angle1\)

Substitute \(m\angle4 = 122^{\circ}\) into the formula \(m\angle1 = 180 - 122\). So \(m\angle1=58^{\circ}\)

Answer:

\(m\angle1 = 58^{\circ}\)