Question

Please help me with this homework!

Answer 1

Part 1: Define

Part 1i) Defining "adjacent angles"

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.

Part 1ii) Defining "vertical angles"

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.

Part 2: Solve

Problem 8:

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 $\square$, 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°.

Problem 9:

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°.

Problem 10:

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;

• 117 + ∠x = 180°

When isolating x, we get;

• ⇒ 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