A) \[90{}^\circ ,\]\[40{}^\circ ,\]\[50{}^\circ \]
B) \[90{}^\circ ,\]\[55{}^\circ ,\]\[35{}^\circ \]
C) \[90{}^\circ ,\]\[60{}^\circ ,\]\[30{}^\circ \]
D) None of these
Correct Answer: A
Solution :
[a] In a\[\Delta \], sum of internal angles \[=180{}^\circ \] \[\therefore \,\,\angle A+\angle B+\angle C=180{}^\circ \] ? (1) It is given that \[\therefore \,\,\angle A=\angle B+\angle C\] ? (2) From (1) and (2) \[\angle A+\angle A=180{}^\circ \] \[\Rightarrow \] \[2\angle A=180{}^\circ \] \[\Rightarrow \] \[\angle A=90{}^\circ \] Let \[\angle B=4x\] \[\angle C=5x\] \[\therefore \] \[\angle B+\angle C=90{}^\circ \] \[4x+5x=90{}^\circ \] \[x=10{}^\circ \] \[\therefore \] \[\angle B=40{}^\circ \] \[\therefore \] \[\angle C=50{}^\circ \] \[\therefore \] Angles are \[90{}^\circ ,\] \[40{}^\circ ,\] \[50{}^\circ ,\]
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