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

Verified step by step guidance

1. Recall that complementary angles are two angles whose measures add up to 90 degrees. So, set up the equation: \( (9x + 6) + 3x = 90 \).
2. Combine like terms on the left side of the equation: \( 9x + 6 + 3x = 90 \) becomes \( 12x + 6 = 90 \).
3. Isolate the variable term by subtracting 6 from both sides: \( 12x = 90 - 6 \) which simplifies to \( 12x = 84 \).
4. Solve for \(x\) by dividing both sides by 12: \( x = \frac{84}{12} \).
5. Once you find \(x\), substitute it back into the expressions for the angles \$9x + 6\( and \)3x$ to find the measure of each marked angle.

Key Concepts

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. Understanding this relationship allows you to set up an equation where the sum of the given angle expressions equals 90, which is essential for solving for the variable.

Algebraic Expressions in Angle Measures

Angles can be represented using algebraic expressions involving variables. To find the actual angle measures, you need to translate the problem into an equation and solve for the variable, then substitute back to find each angle's measure.

Solving Linear Equations

Solving for the variable requires knowledge of linear equations. You combine like terms, isolate the variable, and solve the equation to find its value, which then helps determine the numerical values of the angles.