Ex.2. ABC is a triangle. The bisect...
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Ex.2. ABC is a triangle. The bisectors of the internal angle ZB and external angle ZC intersect at D. If ZBDC= 50°, then ZA is (1) 100° (2) 90° (3) 120° (4) 60°

11th - 12th Class
Maths
Solution
107
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So (2) ( A B=A C=A D ) ( Rightarrow angle mathrm{ABC}=angle mathrm{ACB}=30^{circ} ) ( Rightarrow angle B A C=180^{circ}-60^{circ}=120^{circ} ) ( mathrm{Now}, angle mathrm{DAC}=180^{circ}-120^{circ}=60^{circ} ) ( Rightarrow angle A D C+angle A C D=120^{circ} ) ( therefore angle A C D=frac{120^{circ}}{2}=60^{circ} ) ( therefore angle mathrm{BCD}=angle mathrm{ACB}+angle mathrm{ACD} ) ( =30^{circ}+60^{circ}=90^{circ} )
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