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Question

If $$O$$ is centre of circle as shown in figure, find $$\angle RTO$$ if  $$\angle QRT=30^{\circ}$$
1360834_94b3e687b72a4fc6aa72012e6da7db83.png


Solution

The angles on the same line sum up to give $$180$$ 

$$\implies \angle POT+\angle TOQ=180\\\angle TOQ =180-140=40^{\circ}$$

Consider $$\Delta RTO$$

Sum of angles is $$180$$

$$\implies 40+30+\angle RTO=180\\\angle RTO=110^{\circ}$$

Mathematics

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