Question
ABCD is a rhombus such that $\angle\text{ACB}=50^{\circ}.$ Then, $\angle\text{ADB}=?$
- 40°
- 25°
- 65°
- 130°
✓
Answer
- 40°
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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