Question

tell whether the angles are adjacent or vertical. then find the value of x. (section 7.1)
3.
4.
5.

Explanation:

Problem 3

Step1: Identify angle type

The angles are adjacent supplementary angles (they form a straight line, summing to $180^\circ$).

Step2: Set up equation

$x + 34 = 180$

Step3: Solve for x

$x = 180 - 34$
$x = 146$

Problem 4

Step1: Identify angle type

The angles are adjacent complementary angles (they form a right angle, summing to $90^\circ$).

Step2: Set up equation

$x + 74 = 90$

Step3: Solve for x

$x = 90 - 74$
$x = 16$

Problem 5

Step1: Identify angle type

The angles are vertical angles (opposite intersecting angles, equal in measure).

Step2: Set up equation

$x + 10 = 59$

Step3: Solve for x

$x = 59 - 10$
$x = 49$

Answer:

1. The angles are adjacent, $x = 146$
2. The angles are adjacent, $x = 16$
3. The angles are vertical, $x = 49$