MCQ
$ABCD$ is a rhombus such that $\angle\text{ACB}=50^{\circ}.$ Then, $\angle\text{ADB}=?$
- ✓$40^\circ$
- B$25^\circ$
- C$65^\circ$
- D$130^\circ$
✓
Answer
Correct option: A.
$40^\circ$
$ABCD$ is a rhombus.
$\Rightarrow\text{AD || BC}$ and $\text{AC}$ is the transversal.
$\Rightarrow\angle\text{DAC}=\angle\text{ACB}$ (alternate angles)
$\Rightarrow\angle\text{DAC}=50^{\circ}$
In $\triangle\text{AOD},$ by angle sum property,
$\angle\text{AOD}+\angle\text{DAO}+\angle\text{ADO}=180^{\circ}$
$\Rightarrow90^{\circ}+\angle\text{50}^{\circ}+\angle\text{ADO}=180^{\circ}$
$\Rightarrow\angle\text{ADO}=40^{\circ}$
$\Rightarrow\angle\text{ADB}=40^{\circ}$
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