Find the measure of each marked angle. See Example 2 supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees

Key Concepts

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. This concept is crucial for solving problems involving angle relationships, as it allows us to set up equations based on the given angle measures. In this case, the angles 10x + 7 and 7x + 3 are supplementary, meaning their sum equals 180 degrees.

Algebraic Expressions

Algebraic expressions involve variables and constants combined using mathematical operations. In the context of the question, the angles are expressed as algebraic expressions in terms of x. Understanding how to manipulate these expressions is essential for solving for the variable and finding the measures of the angles.

Solving Linear Equations

Solving linear equations involves finding the value of a variable that makes the equation true. In this scenario, after setting up the equation based on the supplementary angles, we will need to isolate x to determine its value. This process is fundamental in trigonometry and algebra, as it allows us to find unknown measures in various geometric contexts.