MCQ
In a parallelogram $\text{ABCD},$ if $\angle\text{DAB}=75^\circ$ and $\angle\text{DBC}=60^\circ,$ then $\angle\text{BDC}=$
- A$75^\circ$
- B$60^\circ$
- ✓$45^\circ$
- D$55^\circ$
✓
Answer
Correct option: C.
$45^\circ$
In parallelogram $\text{ABCD},$
$\angle\text{A}+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-75^\circ=105^\circ$
$\angle\text{ADB}=\angle\text{DBC} \ ($Alternate angles$)$
$\Rightarrow\angle\text{ADB}=60^\circ$
$\angle\text{BDC}=\angle\text{ADC}-\angle\text{ADB}$
$=105^\circ-60^\circ=45^\circ$
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