Question

∠3 is a complement of ∠4, and m∠3 = 46°. find m∠4. ∠7 is a supplement of ∠8, and m∠7 = 109°. find m∠8. ∠uvw and ∠xyz are complementary angles. m∠uvw=(x - 10)°, and m∠xyz=(4x - 10)°. 8. find x. (11x - 8)° (4x - 7)° 7. find the m∠vwx and m∠zwv. (3x+11)° (6x - 15)° m∠vwu = ______ m∠uwt = ____ m∠twx = ______ true or false wu and wx are opposite rays. 10. explain why adjacent angles does not always provide enough information to solve for a missing angle measure. sketch an example. 11. error analysis ∠jkl and ∠xky are vertical angles. find x if m∠jkl=(7x + 2)° and m∠xky=(3x + 10)°. 7x + 2+3x + 10 = 180 10x + 12 = 180 10x = 168 x = 16.8

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. If ∠3 is a complement of ∠4 and m∠3 = 40°, then m∠4=90° - m∠3.
m∠4 = 90 - 40=50°

Step2: Recall supplementary - angle property

Supplementary angles sum to 180°. If ∠7 is a supplement of ∠8 and m∠7 = 100°, then m∠8=180° - m∠7.
m∠8 = 180 - 100 = 80°

Step3: Use complementary - angle property for ∠UVW and ∠XYZ

Since ∠UVW and ∠XYZ are complementary, m∠UVW + m∠XYZ=90°.
(x - 10)+(4x - 10)=90
5x-20 = 90
5x=90 + 20
5x = 110
x = 22

Step4: For the triangle in question 8

The sum of the interior angles of a triangle is 180°.
(11x - 8)+(4x - 7)+180 - 180=180 (the third - angle is on a straight - line, so its supplementary part is considered).
11x-8 + 4x-7=180
15x-15 = 180
15x=180 + 15
15x = 195
x = 13

Step5: For vertical angles in question 11

Vertical angles are equal. So, 7x + 2=3x + 10
7x-3x=10 - 2
4x=8
x = 2

Answer:

m∠4 = 50°
m∠8 = 80°
x (for ∠UVW and ∠XYZ)=22
x (for the triangle)=13
x (for vertical angles ∠JKL and ∠XKY)=2