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;
- 117 + ∠x = 180°
<u>When isolating x, we get;</u>
- ⇒ 117 + ∠x - 117 = 180° - 117
- ⇒ ∠x = 180° - 117
- ⇒ ∠x = 63°
Therefore, the measure of ∠x is 63°
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