As a manufacturing technician programming a CNC machine, you are working on a part where two adjacent angles form a straight edge, meaning you must recall they are supplementary. The design blueprint specifies that the larger angle is exactly 18 degrees less than twice the smaller angle. If $x$ represents the smaller angle, which equation correctly recalls the geometric rule and shows the proper substitution step required to solve for $x$?

A technician is installing a custom countertop where two surface pieces meet along a straight wall, creating two supplementary angles. The blueprint indicates the larger angle is 18 degrees less than twice the smaller angle. Arrange the following steps in the correct logical order to solve for both angle measures using the substitution method.

A carpenter is framing a roof where two rafters meet at a peak along a straight ridge beam, forming two supplementary angles. If $x$ represents the smaller angle and $y$ represents the larger angle, match each geometric or verbal description with its correct algebraic representation.

A metal fabricator is cutting a steel plate where two angles meet along a straight edge, making them supplementary. If the larger angle is 18 degrees less than twice the smaller angle $x$, the technician correctly recalls that the relationship can be modeled by the equation $x + (2x - 18) = 180$.

Recalling Algebraic Translations for Supplementary Angles

An HVAC technician is installing a custom sheet-metal duct that bends along a straight wall, creating two supplementary angles. The design blueprint specifies that the measure of the larger angle of the bend is exactly 18 degrees less than twice the measure of the smaller angle, represented by $x$.

To represent the measure of the larger angle, the technician translates this specification into an algebraic expression. Recalling the rules of algebraic translation, write the expression for the larger angle in terms of $x$.

(Do not include spaces, degree symbols, or equals signs in your answer, e.g., write your answer in the format 2x-18.)

Recalling Equations for an Intersection Design