Question

special pairs of angles practice directions - complete the following problems; show all work; put your answers on your answer sheet. 1. ∠yoz & ∠woy are complementary m∠woy = 19x - 26 m∠yoz = 10x find the following: x = __________ m∠woy = ________ m∠yoz = ________ m∠woz = ________ 2. find the following: x = ________ m∠ram = ________ m∠man = ________ m∠ran = ________ 3. qb is the angle bisector of ∠aqc. m∠aqb = 5x m∠bqc = 8x - 24 find the following: x = ________ m∠aqb = ________ m∠bqc = ________ m∠aqc = ________ 4. m∠tpq = 90° m∠qps = 7x - 12 m∠spr = 5x + 6 find the following: x = ________ m∠tpr = ________ m∠qps = ________ m∠spr = ________ m∠qpr = ________ m∠spt = __________

Explanation:

Problem 1: Complementary angles sum to 90°

$(19x - 26) + 10x = 90$
$29x = 116$
$x = 4$
$m∠WOY = 19(4) - 26 = 50°$
$m∠YOZ = 10(4) = 40°$
$m∠WOZ = 50° + 40° = 90°$

Problem 2: Straight angle sum to 180°

$(50x - 10) + (8x + 16) = 180$
$58x = 174$
$x = 3$
$m∠RAM = 50(3) - 10 = 140°$
$m∠MAN = 8(3) + 16 = 40°$
$m∠RAN = 180°$

Problem 3: Angle bisector creates equal angles

$5x = 8x - 24$
$3x = 24$
$x = 8$
$m∠AQB = 5(8) = 40°$
$m∠BQC = 8(8) - 24 = 40°$
$m∠AQC = 40° + 40° = 80°$

Problem 4: Right angle ∠QPR = 90°

$(7x - 12) + (5x + 6) = 90$
$12x = 96$
$x = 8$
$m∠TPR = 180°$
$m∠QPS = 7(8) - 12 = 44°$
$m∠SPR = 5(8) + 6 = 46°$
$m∠QPR = 90°$
$m∠SPT = 180° - 46° = 134°$

Answer:

Problem 1: x = 4, m∠WOY = 50°, m∠YOZ = 40°, m∠WOZ = 90°
Problem 2: x = 3, m∠RAM = 140°, m∠MAN = 40°, m∠RAN = 180°
Problem 3: x = 8, m∠AQB = 40°, m∠BQC = 40°, m∠AQC = 80°
Problem 4: x = 8, m∠TPR = 180°, m∠QPS = 44°, m∠SPR = 46°, m∠QPR = 90°, m∠SPT = 134°