Question

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

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.)$$\Rightarrow y + 50^{\circ} + 53^{\circ} = 180^{\circ}$$$$\Rightarrow y + 103^{\circ} = 180^{\circ}$$$$\Rightarrow y = 77^{\circ}$$$$\therefore\ x=50^{\circ},y=77^{\circ}$$MathematicsRS AgarwalStandard IX

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