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Question Number 170012 by cortano1 last updated on 14/May/22

	Answered by som(math1967) last updated on 14/May/22

	$F r o m △ A B C$ $\frac{A C}{s i n 50} = \frac{B C}{s i n 30} [∵ ∡ A B C = 180 - 100 - 30 = 50]$ $f r o m △ D B C$ $\frac{B D}{s i n 100} = \frac{B C}{s i n x}$ $\frac{B D}{s i n 50} = \frac{B C}{s i n x s i n 50} \times s i n (180 - 80)$ $\frac{B D}{s i n 50} = \frac{s i n 80 B C}{s i n x s i n 50}$ $\frac{A C}{s i n 50} = \frac{s i n 80 B C}{s i n x s i n 50}$ $\frac{B C}{s i n 30} = \frac{2 s i n 40 c o s 40 B C}{s i n x c o s 40}$ $s i n x = s i n 40 ∴ x = 40$
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