Question

1.6 practice with calcchat and calcview
in exercises 1 - 4, use the diagrams. (see example 1.)

1. name a pair of adjacent complementary angles.
2. name a pair of adjacent supplementary angles.
3. name a pair of nonadjacent supplementary angles.
4. name a pair of nonadjacent complementary angles.

in exercises 5 - 8, find the angle measure. (see example 2.)

1. ∠1 is a complement of ∠2, and m∠1 = 23°. find m∠2.
2. ∠3 is a complement of ∠4, and m∠3 = 46°. find m∠4.
3. ∠5 is a supplement of ∠6, and m∠5 = 78°. find m∠6.
4. ∠7 is a supplement of ∠8, and m∠7 = 109°. find m∠8.

in exercises 9 - 12, find the measure of each angle. (see example 3.)
9.
10.

1. ∠uvw and ∠xyz are complementary angles, m∠uvw=(x - 10)°, and m∠xyz=(4x - 10)°.
2. ∠efg and ∠lmn are supplementary angles, m∠efg=(3x + 17)°, and m∠lmn=(\frac{1}{2}x - 5)°.

1.6 describing pairs of angles

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°.

Step2: Solve for Exercise 5

If ∠1 is a complement of ∠2 and m∠1 = 23°, then m∠2=90° - m∠1. So m∠2 = 90° - 23°=67°.

Step3: Recall complementary - angle property for Exercise 6

If ∠3 is a complement of ∠4 and m∠3 = 46°, then m∠4=90° - m∠3. So m∠4 = 90° - 46° = 44°.

Step4: Recall supplementary - angle property

Supplementary angles add up to 180°.

Step5: Solve for Exercise 7

If ∠5 is a supplement of ∠6 and m∠5 = 78°, then m∠6=180° - m∠5. So m∠6 = 180° - 78°=102°.

Step6: Solve for Exercise 8

If ∠7 is a supplement of ∠8 and m∠7 = 109°, then m∠8=180° - m∠7. So m∠8 = 180° - 109° = 71°.

Step7: For Exercise 9

Since (3x + 5)° and (10x - 7)° are supplementary (linear - pair), (3x + 5)+(10x - 7)=180. Combine like terms: 13x - 2 = 180. Add 2 to both sides: 13x=182. Divide by 13: x = 14. Then 3x + 5=3(14)+5 = 42 + 5=47° and 10x - 7=10(14)-7 = 140 - 7 = 133°.

Step8: For Exercise 10

Since (15x - 2)° and (7x+4)° are complementary, (15x - 2)+(7x + 4)=90. Combine like terms: 22x+2 = 90. Subtract 2 from both sides: 22x = 88. Divide by 22: x = 4. Then 15x - 2=15(4)-2 = 60 - 2 = 58° and 7x + 4=7(4)+4 = 28 + 4 = 32°.

Step9: For Exercise 11

Since ∠UVW and ∠XYZ are complementary, (x - 10)+(4x - 10)=90. Combine like terms: 5x-20 = 90. Add 20 to both sides: 5x = 110. Divide by 5: x = 22. Then m∠UVW=x - 10=22 - 10 = 12° and m∠XYZ=4x - 10=4(22)-10 = 88 - 10 = 78°.

Step10: For Exercise 12

Since ∠EFG and ∠LMN are supplementary, (3x + 17)+(\(\frac{1}{2}x-5\))=180. Combine like terms: \(3x+\frac{1}{2}x+17 - 5=180\), \(\frac{6x + x}{2}+12 = 180\), \(\frac{7x}{2}=168\). Multiply both sides by \(\frac{2}{7}\): x = 48. Then m∠EFG=3x + 17=3(48)+17 = 144+17 = 161° and m∠LMN=\(\frac{1}{2}x - 5=\frac{1}{2}(48)-5 = 24 - 5 = 19°\).

Answer:

1. m∠2 = 67°
2. m∠4 = 44°
3. m∠6 = 102°
4. m∠8 = 71°
5. The angles are 47° and 133°
6. The angles are 58° and 32°
7. m∠UVW = 12°, m∠XYZ = 78°
8. m∠EFG = 161°, m∠LMN = 19°