Question

tell whether the angles are complementary or supplementary. then find the value of x. (section 7.2)
6.
7.

Explanation:

For Problem 6:

Step1: Identify angle type (supplementary)

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

Step2: Set up supplementary angle equation

$$(2x + 5) + 75 = 180$$

Step3: Simplify and solve for $x$

$$2x + 80 = 180$$
$$2x = 180 - 80$$
$$2x = 100$$
$$x = \frac{100}{2} = 50$$

Step1: Identify angle type (complementary)

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

Step2: Set up complementary angle equation

$$x + (3x - 6) = 90$$

Step3: Simplify and solve for $x$

$$4x - 6 = 90$$
$$4x = 90 + 6$$
$$4x = 96$$
$$x = \frac{96}{4} = 24$$

Answer:

The angles are supplementary, and $x = 50$

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For Problem 7: