Question

1. examine the given what is the measure of angle anp? 31° 141° 131° 18°

Explanation:

Step1: Find adjacent angles on straight lines

First, find the supplementary angles to \(162^\circ\) and \(149^\circ\) on the straight lines. For the angle at \(A\), the adjacent angle (let's call it \(\angle PAM\)) is \(180^\circ - 162^\circ = 18^\circ\). For the angle at \(B\), the adjacent angle (let's call it \(\angle PBN\)) is \(180^\circ - 149^\circ = 31^\circ\).

Step2: Use the sum of angles in a triangle (or quadrilateral? Wait, actually, in the figure, if we consider the triangle or the angle sum around the point, but more accurately, in a triangle, the sum of angles is \(180^\circ\), but here we have a quadrilateral? Wait, no, the angle \(\angle ANP\) is in a triangle? Wait, maybe the figure is a triangle with two exterior angles? Wait, no, let's re - evaluate. Wait, the sum of the two supplementary angles and the angle we want? Wait, no, the formula for the measure of an angle in a triangle with two exterior angles: the measure of the angle (let's say \(\angle ANP\)) can be found by \(180^\circ-(18^\circ + 31^\circ)\)? Wait, no, that's not right. Wait, actually, the sum of the two given angles ( \(162^\circ\) and \(149^\circ\)) minus \(180^\circ\) gives the angle? Wait, \(162 + 149-180=131^\circ\)? Wait, let's do it properly.

The sum of the interior angles of a triangle is \(180^\circ\). The two angles adjacent to the exterior angles are \(180 - 162=18^\circ\) and \(180 - 149 = 31^\circ\). Then the third angle of the triangle (the angle opposite to \(\angle ANP\))? Wait, no, maybe the figure is a quadrilateral? Wait, no, the angle \(\angle ANP\) is equal to \(162^\circ+149^\circ - 180^\circ\). Let's calculate that: \(162 + 149=311\), \(311-180 = 131^\circ\).

Answer:

\(131^\circ\) (corresponding to the option with \(131^\circ\))