Question

8.5 the student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.

1. name pairs of vertical, adjacent, supplementary, and complementary angles.

use the diagram to answer questions 2 - 5.

1. name the pairs of vertical angles in the figure.
2. which two angles are supplementary?
3. name an angle in the figure that is adjacent to angle 2.
4. which pairs of angles are complementary?
5. solve for x.

a. x = 27 b. x = 18 c. x = 78 d. x = 6.75

Explanation:

Step1: Set up the equation

Since the two angles \(3x + 24\) and \(5x+12\) are supplementary (they form a linear - pair, and the sum of angles in a linear - pair is \(180^{\circ}\)), we have the equation \((3x + 24)+(5x + 12)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+5x+24 + 12=180\), which simplifies to \(8x+36 = 180\).

Step3: Isolate the term with \(x\)

Subtract 36 from both sides of the equation: \(8x+36-36=180 - 36\), so \(8x=144\).

Step4: Solve for \(x\)

Divide both sides by 8: \(x=\frac{144}{8}=18\).

Answer:

\(x = 18\) (Option B)