Mathematics

Find $$\angle APB$$, if $$AE || BR$$.


SOLUTION
given $$AE\parallel BR$$
Now AB acts as transversal. 
$$\angle A+\angle B=180^{\circ}$$ (interior angles of same side of transversal are supplementary ) 
$$\therefore 2x+2y=180^{\circ}$$
$$2(x+y)=180^{\circ}$$ 
$$x+y=90^{\circ}$$ 
Now in $$\Delta APB$$
$$\angle PAB+\angle PBA+\angle APB=180^{\circ}$$ 
$$X+Y+\angle APB=180^{\circ}$$ 
But $$x+y=90^{\circ}$$ 
$$\therefore \angle APB=180^{\circ}-(x+y)$$ 
$$\angle APB=180^{\circ}-90^{\circ}$$ 
$$\angle APB=90^{\circ}$$
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