Find the measure of each marked angle. See Example 2complementary angles with measures 9𝓍 + 6 and 3𝓍 degrees

Complementary angles are two angles whose measures add up to 90 degrees. In this problem, the angles given are expressed in terms of a variable, x, and their sum must equal 90 degrees to satisfy the definition of complementary angles. Understanding this concept is crucial for setting up the equation needed to solve for x.

Algebraic expressions involve variables and constants combined using mathematical operations. In this question, the angles are represented as algebraic expressions (9x + 6 and 3x). To find the measures of the angles, one must manipulate these expressions through algebraic techniques, such as combining like terms and solving for the variable.

Solving linear equations involves finding the value of a variable that makes the equation true. In this case, after setting up the equation based on the complementary angles, you will need to isolate x to determine its value. This process often includes steps like simplifying both sides of the equation and applying inverse operations.