Question

name the relationship: complementary, linear pair, vertical, or adjacent. 7) 8) a) consecutive interior b) corresponding c) alternate exterior d) linear pair a) vertical b) alternate exterior c) linear pair d) alternate interior find the value of x. 9) 10) (2x + 15)° 119° 72° 3x°

Explanation:

Step1: Identify angle - relationship for 7

The angles in question 7 are vertical angles. Vertical angles are formed when two lines intersect and are opposite each other. They are equal in measure.

Step2: Identify angle - relationship for 8

The angles in question 8 are vertical angles as they are opposite each other at the intersection of two lines.

Step3: Solve for x in 9

The two angles are supplementary (a linear - pair), so their sum is 180°.
Set up the equation: \((2x + 15)+119=180\).
First, simplify the left - hand side: \(2x+134 = 180\).
Then, subtract 134 from both sides: \(2x=180 - 134=46\).
Finally, divide both sides by 2: \(x = 23\).

Step4: Solve for x in 10

The two angles are vertical angles, so they are equal.
Set up the equation: \(3x=72\).
Divide both sides by 3: \(x = 24\).

Answer:

1. A. vertical
2. A. vertical
3. \(x = 23\)
4. \(x = 24\)