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Question

In the figure, if $$AB\parallel CD,\angle APQ={ 50 }^{ }$$ and $$\angle PRD={ 127 }^{ }$$, find $$x$$ and $$y$$.
463661.jpg


Solution

Given, $$AB \parallel CD, \angle APQ = 50^{\circ}, \angle PRD = 127^{\circ}$$
According to the question 

$$x = 50^{\circ}$$ (Alternate interior angles.)

$$\angle PRD + \angle RPB = 180^{\circ}$$ (Angles on the same side of transversal.)

$$\Rightarrow  127^{\circ} + \angle RPB = 180^{\circ}$$

$$\Rightarrow \angle RPB = 53^{\circ}$$ 

Now, $$y + 50^{\circ} + \angle RPB = 180^{\circ}$$ ($$AB$$ is a straight line.)

$$\Rightarrow  y + 50^{\circ} + 53^{\circ} = 180^{\circ}$$

$$\Rightarrow  y + 103^{\circ} = 180^{\circ}$$

$$\Rightarrow  y = 77^{\circ}$$

$$\therefore\ x=50^{\circ},y=77^{\circ}$$

Mathematics
RS Agarwal
Standard IX

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