A) \[50{}^\circ \]
B) \[60{}^\circ \]
C) \[70{}^\circ \]
D) \[80{}^\circ \]
Correct Answer: C
Solution :
Let required angle be \[\theta \] From geometry of figure In \[\Delta ABC, \alpha =180{}^\circ - \left( 60{}^\circ + 40{}^\circ \right) = 80{}^\circ \] \[\Rightarrow \,\,\,\,\,\beta \,\,=\,\,90{}^\circ -80{}^\circ =10{}^\circ \] \[\operatorname{In}\,\,\,\,\,\,\,\,\,\,\Delta \,ABD, \angle A = 60{}^\circ , \angle B=(\alpha +2\,\beta )\] \[= \left( 80 + 2 \times 10 \right)\,\,=\,\,100{}^\circ \,\,and\,\,\angle D- (90{}^\circ -\theta )\] \[\because \,\,\,\,\,\,\,\angle A+\angle B+\angle D=180{}^\circ \] \[\Rightarrow \,\,\,\,\,\,60{}^\circ +100{}^\circ +\left( 90{}^\circ -\,\,\theta \right) =180{}^\circ \] \[\Rightarrow \,\,\,\,\,\,\,\,\theta =70{}^\circ \]You need to login to perform this action.
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