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°

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