In the figure, $ABCD$ is a parallelogram. Given that $\angle DAB=64{}^\circ $, \(\angle CMB

Question

In the figure, $ABCD$ is a parallelogram. Given that $\angle DAB=64{}^\circ $, $\angle CMB=70{}^\circ $ and $\angle BCM=36{}^\circ $. Find $\angle BCD$, $\angle CBM$, $\angle BDC$, stating your reasons clearly. Source consistency note: The exact angle labels are inconsistent with a parallelogram. The angle chase gives $\angle BAM=28^\circ,\angle ABM=42^\circ,\angle CBM=74^\circ$. The sine rule gives $AM/BM=\sin42^\circ/\sin28^\circ$, but $CM/BM=\sin74^\circ/\sin36^\circ$; these are unequal, contradicting $AM=CM$. The numerical answers below are conditional angle-chasing results, not angles of a figure satisfying every label.

Accepted Answer

(a) $64^\circ$; (b) $74^\circ$; (c) $42^\circ$. The results are conditional; the exact source labels conflict.

Parallelogram

Parallelogram

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