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TP is a line that tangent to a circle centered at O. If PQ∥TO and ∠OTP=25∘, find the measure of ∠POQ in degrees.

 

 Jun 16, 2020
 #1
avatar+1361 
+2

∠PTO = 25º

 

∠TOP = ∠OPQ = ∠OQP = 65º

 

∠QOP = 50º

 

∠POQ = ∠QOP     laugh

 Jun 16, 2020
edited by Dragan  Jun 16, 2020
 #2
avatar+25569 
+2

TP is a line that tangent to a circle centered at \(O\).
If \(PQ\parallel TO\) and \(\angle OTP=25^\circ\), find the measure of \(\angle POQ\) in degrees.

 

\(\begin{array}{|rcll|} \hline \hline \mathbf{65^\circ} &=& \mathbf{90^\circ-\dfrac{x}{2}} \\\\ \dfrac{x}{2} &=& 90^\circ-65^\circ \\\\ \dfrac{x}{2} &=& 25^\circ \\\\ \mathbf{x} &=& \mathbf{50^\circ} \\ \end{array}\)

 

laugh

 Jun 16, 2020

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