SOLUTION: In the diagram ∠TPQ = ∠SPR and TP ⊥ SR. Find the measure of ∠SRP Image: https://imgur.com/a/OOlwEo2

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Question 1199664: In the diagram ∠TPQ = ∠SPR and TP ⊥ SR. Find the measure of ∠SRP
Image: https://imgur.com/a/OOlwEo2
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200) About Me  (Show Source):
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The drawing on the site is not to scale. This one is:



Extend TP to U



∠TPQ = ∠UPR because they are vertical angles.

∠TPQ = ∠SPR = ∠UPR

PR bisects ∠UPS

ΔSUP is a right triangle

∠UPS is complementary to ∠USP = 41o

∠UPS = 90o - 41o = 49o

∠RPS is half of ∠UPS, and half of 49o is 24.5o  

We now know two angles of ΔSRP, 24.5o and 41o,

So we add them and subtract from 180o.

∠SRP = 180o-(24.5o+41o) = 114.5o

Edwin