MCQ
In the given figure, $\angle\text{BAC}=40^\circ,\angle\text{ACB}=90^\circ$ and $\angle\text{BED}=100^\circ,$ Then $\angle\text{BDE}=?$
- A$50^\circ$
- B$40^\circ$
- C$25^\circ$
- ✓$30^\circ$
✓
Answer
Correct option: D.
$30^\circ$
In $\triangle\text{ABC}$$\angle\text{ABC}+\angle\text{BAC}+\angle\text{ACB}=180^\circ$ (Angle sum property)
$\angle\text{ABC}=180^\circ-90^\circ-40^\circ$
$\angle\text{ABC}=50^\circ$
In $\angle\text{BED}$
$\angle\text{BED}+\angle\text{EBD}+\angle\text{BDE}=180^\circ$ (Angle sum property)
$\angle\text{BDE}=180^\circ-50^\circ-100^\circ$
$\angle\text{BDE}=30^\circ.$
$\angle\text{ABC}=180^\circ-90^\circ-40^\circ$
$\angle\text{ABC}=50^\circ$
In $\angle\text{BED}$
$\angle\text{BED}+\angle\text{EBD}+\angle\text{BDE}=180^\circ$ (Angle sum property)
$\angle\text{BDE}=180^\circ-50^\circ-100^\circ$
$\angle\text{BDE}=30^\circ.$
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