<h2><u>Part 1: Define</u></h2><h3>Part 1i) Defining "adjacent angles"</h3>

In this case, adjacent angles are such pairs of angles that are alongside each other. Therefore, we can say that the sum of the two adjacent angles forms a **bigger angle. **

<h3>Part 1ii) Defining "vertical angles"</h3>

In this case, vertical angles are such angles that are on opposite sides of the intersection between two lines. It is understood that vertically opposite angles are **equivalent. **

<h2><u>Part 2: Solve</u></h2><h3>Problem 8:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are** alongside each other. **Therefore, we can tell the angles are adjacent angles.

As we can see a , we can tell that the sum of the measure of ∠x and the other angle is 90°. Therefore, we obtained;

- ⇒ ∠x + 35 = 90
- ⇒ ∠x = 90 - 35
- ⇒ ∠x = 65°

Therefore, the measure of **∠x** is **65°.**

<h3 /><h3>Problem 9:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are** on opposite sides. **Therefore, we can tell that the angles are vertically opposite angles.

As stated in part 1ii, vertical angles are equivalent. Since ∠x and the other angles are vertically opposite angles, the measure of **∠x **is** 128°.**

<h3 /><h3>Problem 10:</h3>

Clearly, we can see that two angles (one angle known as ∠x and the other angle) are** alongside each other. **Therefore, we can tell the angles are adjacent angles.

Since the line shown, is a straight line, we can tell that the sum of 117 and x is 180. Therefore, we obtain the following equation;

<u>When isolating x, we get;</u>

- ⇒ 117 + ∠x - 117 = 180° - 117
- ⇒ ∠x = 180° - 117
- ⇒ ∠x = 63°

Therefore, the measure of **∠x** is** 63°**

**Learn more **about this topic: brainly.com/question/14355129