Question

1. ∠abc and ∠cbd are adjacent angles. which side do the angles have in common? 1 tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. 3. ∠1 and ∠2 4. ∠1 and ∠3 5. ∠2 and ∠4 6. ∠2 and ∠3 2 find the measure of each of the following. 7. supplement of ∠a 8. complement of ∠a 9. supplement of ∠b 10. complement of ∠b 3 11. multi - step an angles measure is 6 degrees more than 3 times the measure of its complement. find the measure of the angle.

Explanation:

Step1: Recall angle - pair definitions

Adjacent angles share a common side and a common vertex. A linear - pair of adjacent angles is such that their non - common sides form a straight line. Complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees.

Step2: Analyze adjacent angles for 3 - 6

• For ∠1 and ∠2: They are adjacent and form a linear pair since their non - common sides form a straight line.
• For ∠1 and ∠3: They are not adjacent as they do not share a common side.
• For ∠2 and ∠4: They are not adjacent as they do not share a common side.
• For ∠2 and ∠3: They are adjacent but do not form a linear pair.

Step3: Calculate supplements and complements for 7 - 10

• The supplement of ∠A with measure 81.2° is 180°−81.2° = 98.8°.
• The complement of ∠A with measure 81.2° is 90°−81.2° = 8.8°.
• Let the measure of ∠B=(6x - 5)°. The supplement of ∠B is 180°-(6x - 5)°=(185 - 6x)°. The complement of ∠B is 90°-(6x - 5)°=(95 - 6x)°.

Step4: Solve for the angle in 11

Let the angle be y and its complement be 90 - y.
We are given that y=3(90 - y)+6.
Expand the right - hand side: y = 270-3y + 6.
Add 3y to both sides: y+3y=270 + 6.
4y=276.
Divide both sides by 4: y = 69°.

Answer:

1. Adjacent and form a linear pair
2. Not adjacent
3. Not adjacent
4. Adjacent but not a linear pair
5. 98.8°
6. 8.8°
7. (185 - 6x)°
8. (95 - 6x)°
9. 69°