Question

bentley wendts p... d.4 transversals of parallel lines: find angle measures
24
look at this diagram:
if \\( \overleftrightarrow { l n } \\) and \\( \overleftrightarrow { o q } \\) are parallel lines and \\( m \angle n m k = 47 ^ { \circ } \\), what is \\( m \angle l m p \\)?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. Since \(\angle NMK\) and \(\angle PMQ\) are vertical angles, \(m\angle PMQ=m\angle NMK = 47^{\circ}\).

Step2: Use the property of supplementary angles

\(\angle LMP\) and \(\angle PMQ\) are supplementary (they form a linear - pair). The sum of supplementary angles is \(180^{\circ}\). So \(m\angle LMP=180^{\circ}-m\angle PMQ\).
Substitute \(m\angle PMQ = 47^{\circ}\) into the formula: \(m\angle LMP=180 - 47\).

Answer:

\(133\)