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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
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∠PTO = 25º

∠TOP = ∠OPQ = ∠OQP = 65º

∠QOP = 50º

∠POQ = ∠QOP

Jun 16, 2020
edited by Dragan  Jun 16, 2020
#2
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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.

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

Jun 16, 2020