Question

two angles whose measures have a sum of 180° have a supplementary relationship. b. ∠lmn at left is called a straight angle (or the two combined are called linear angles). if m∠lmp = 62°, what is m∠pmn? show your calculations.

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). So \(m\angle LMP + m\angle PMN = 180^\circ\).

Step2: Substitute known value

Given \(m\angle LMP = 62^\circ\), substitute into the equation: \(62^\circ + m\angle PMN = 180^\circ\).

Step3: Solve for \(m\angle PMN\)

Subtract \(62^\circ\) from both sides: \(m\angle PMN = 180^\circ - 62^\circ = 118^\circ\).

Answer:

\(118^\circ\)