Question

chapter 2 lines, angles, and quadrilaterals
2.3 complementary and supplementary angles (dok 2)
two angles are complementary if the sum of the measures of the angles is 90°.
two angles are supplementary if the sum of the measures of the angles is 180°.
two angles along a straight line are supplementary.
the angles may be adjacent but do not need to be
(images of complementary angles and supplementary angles)
calculate the measure of each unknown angle.
(images of angle diagrams with labeled angles and unknowns)

1. ∠a = ____ 5. ∠e = ____
2. ∠b = ____ 6. ∠f = ____
3. ∠c = ____ 7. ∠g = ____
4. ∠d = ____ 8. ∠h = ____

(images of three more angle diagrams with labeled angles and unknowns)

1. ∠aob = ____ 13. ∠rms = __ 17. ∠ajk = ____
2. ∠cod = ____ 14. ∠vmt = __ 18. ∠ckd = ____
3. ∠eof = ____ 15. ∠qmn = __ 19. ∠fkh = ____
4. ∠aoh = ____ 16. ∠wpq = __ 20. ∠blc = ____

Explanation:

Step1: Solve for angles 1-8 (intersecting lines)

∠a (supplementary to 140°)

$\angle a = 180^\circ - 140^\circ = 40^\circ$

∠b (vertical to 140°)

$\angle b = 140^\circ$

∠c (vertical to ∠a)

$\angle c = \angle a = 40^\circ$

∠d (supplementary to 119°)

$\angle d = 180^\circ - 119^\circ = 61^\circ$

∠e (vertical to ∠d)

$\angle e = \angle d = 61^\circ$

∠f (supplementary to 159°)

$\angle f = 180^\circ - 159^\circ = 21^\circ$

∠g (vertical to 159°)

$\angle g = 159^\circ$

∠h (vertical to 119°)

$\angle h = 119^\circ$

Step2: Solve for angles 9-12 (point O)

∠AOB (right angle minus 53°)

$\angle AOB = 90^\circ - 53^\circ = 37^\circ$

∠COD (right angle minus 74°)

$\angle COD = 90^\circ - 74^\circ = 16^\circ$

∠EOF (vertical to ∠AOB)

$\angle EOF = \angle AOB = 37^\circ$

∠AOH (right angle minus 61°)

$\angle AOH = 90^\circ - 61^\circ = 29^\circ$

Step3: Solve for angles 13-16 (point M)

∠RMS (right angle minus 21°)

$\angle RMS = 90^\circ - 21^\circ = 69^\circ$

∠VMT (supplementary to 90°+62°)

$\angle VMT = 180^\circ - (90^\circ+62^\circ) = 28^\circ$

∠QMN (supplementary to 99°)

$\angle QMN = 180^\circ - 99^\circ = 81^\circ$

∠WPQ (vertical to ∠VMT)

$\angle WPQ = \angle VMT = 28^\circ$

Step4: Solve for angles 17-20 (points J/K)

∠AJK (supplementary to 49°)

$\angle AJK = 180^\circ - 49^\circ = 131^\circ$

∠CKD (right angle minus 55°)

$\angle CKD = 90^\circ - 55^\circ = 35^\circ$

∠FKH (vertical to ∠AJK)

$\angle FKH = \angle AJK = 131^\circ$

∠BLC (supplementary to 45°+47°)

$\angle BLC = 180^\circ - (45^\circ+47^\circ) = 88^\circ$

Answer:

1. $\angle a = 40^\circ$
2. $\angle b = 140^\circ$
3. $\angle c = 40^\circ$
4. $\angle d = 61^\circ$
5. $\angle e = 61^\circ$
6. $\angle f = 21^\circ$
7. $\angle g = 159^\circ$
8. $\angle h = 119^\circ$
9. $\angle AOB = 37^\circ$
10. $\angle COD = 16^\circ$
11. $\angle EOF = 37^\circ$
12. $\angle AOH = 29^\circ$
13. $\angle RMS = 69^\circ$
14. $\angle VMT = 28^\circ$
15. $\angle QMN = 81^\circ$
16. $\angle WPQ = 28^\circ$
17. $\angle AJK = 131^\circ$
18. $\angle CKD = 35^\circ$
19. $\angle FKH = 131^\circ$
20. $\angle BLC = 88^\circ$