In the diagram shown, it is known that segment RP is perpendicular to segment QS and segment RP bisects angle SRQ. If measure angle SRQ=104 degrees, then explain why measure angle S=38 degrees.

*attachment contains the missing diagram

Answer/Step-by-step explanation:

Given that RP ⟂ QS, <RPS is a right angle.

Therefore, m<RPS = 90°

Since RP bisects <SRQ, therefore m<PRS = ½ of m<SRQ.

Therefore:

m<PRS = ½*104°

m<PRS = 52°

m<S + m<RPS + m<PRS = 180° (sum of ∆)

m<S + 90° + 52° = 180° (substitution)

m<S + 142 = 180°

Subtract 142 from each side

m<S = 180° - 142°

m<S = 38°

step-by-step explanation:

is their an equation anywhere i can take a   look at it and see if i am right.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.