All of the following must be true statements except:

m∠rps = m ∠wpr
m∠rps + m∠ spu= 180
m∠ spt = m∠ upt

We need to find the false statement.

The first one is true (m<RPS=m<WPR because RU⊥SW).

The second statement is true because the two angles make a linear pair and are supplementary.

The third one is false because we only know that the angle pair is complimentary. Their measures are not equal.

m∠SPT=m∠UPT

answer:   y=2x-3

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west