Mathematics

In the figure.$$A B \parallel C D$$ , $$\angle P T B = 55 ^ { \circ }$$ and $$\angle D V S = 45 ^ { \circ }$$.
 Find sum of $$\angle \mathrm { CUQ }$$ and $$\angle R T P$$ is :


SOLUTION
Given $$AB\parallel CD\angle PTB=55^{o}, \angle DVS=45^{o}$$

Find : $$\angle CUQ+\angle RTP$$

If $$AB\parallel CD$$ then, 

$$\angle VTB=\angle DVS=45^{o}$$  [corresponding angles]

According to lines pair of angles

$$\angle RTP+\angle PTB+\angle VTB=180^{o}$$

$$\angle RTP+55^{o}+45^{o}=180^{o}$$

$$\angle RTP=80^{o}$$

Then, $$\angle ATC=\angle PTB=55^{o}$$ (vertically opposite angles)

If $$AB\parallel CD$$, then 

$$\angle CUQ=\angle ATC=55^{o}$$

$$\therefore \angle CUQ +\angle RTP=55^{o}+80^{o}=135^{o}$$

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Subjective Medium Published on 09th 09, 2020
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