Question

find x.
37°
x°
92°
x =

Explanation:

Step1: Identify angle relations

The triangle's exterior angle (92°) relates to the two remote interior angles (37° and \( x^\circ \)). By the exterior angle theorem, the exterior angle equals the sum of the two non - adjacent interior angles. Wait, no, actually, first, find the supplementary angle to 92°? Wait, no, let's look at the triangle. The angle adjacent to 92° is \( 180 - 92=88^\circ \)? Wait, no, maybe using the triangle angle sum. Wait, the 37° angle and \( x \) and the angle supplementary to 92° (since they are on a straight line) should sum to 180°? Wait, no, let's correct. The exterior angle theorem: in a triangle, an exterior angle is equal to the sum of the two remote interior angles. Wait, the 92° angle: is it an exterior angle? Wait, the angle inside the triangle adjacent to 92° is \( 180 - 92 = 88^\circ \)? No, maybe I got it wrong. Wait, the three angles in the triangle: 37°, \( x \), and the angle that is supplementary to 92°? Wait, no, let's see the lines. The horizontal line is parallel? Wait, no, the angles: the 37° angle, \( x \), and the angle that is equal to \( 180 - 92=88^\circ \)? Wait, no, let's use the triangle angle sum. The sum of angles in a triangle is 180°. So, if we have a triangle with angles 37°, \( x \), and the angle opposite to the 92° angle (which is vertical or supplementary? Wait, the 92° angle and the angle inside the triangle: they are supplementary? Wait, no, the two lines are intersecting, so the angle adjacent to 92° is \( 180 - 92 = 88^\circ \). Then, in the triangle, we have angles 37°, \( x \), and 88°? Wait, no, that can't be, because 37 + 88=125, 180 - 125 = 55? Wait, no, maybe the exterior angle is 92°, and the two interior angles are 37° and \( x \). Wait, exterior angle theorem: exterior angle = sum of two remote interior angles. So 92°=37°+x? No, that gives x = 92 - 37=55? Wait, let's check. If we have a triangle, and one of its exterior angles is 92°, and one of the non - adjacent interior angles is 37°, then the other non - adjacent interior angle x is 92 - 37=55. Yes, that makes sense.

Step2: Calculate x

Using the exterior angle theorem: \( x=92 - 37 \)
\( x = 55 \)

Answer:

\( x = 55 \)