MCQ
In Fig. if $\text{EC }\|\text{ AB},\angle\text{ECD}=70^\circ$ and $\angle\text{ECD}=70^\circ$ and $\angle\text{BDO}=20^\circ,$ then $\angle\text{OBD}$ is:
- A$20^\circ$
- ✓$50^\circ$
- C$60^\circ$
- D$70^\circ$
✓
Answer
Correct option: B.
$50^\circ$
$EC \| AB$ And, $CD$ is transverse to it.
Now $\angle\text{ECD}=\angle\text{AOD}=70^\circ\ ($Corresponding angles$)$
In $\triangle\text{OBD}$
$\angle\text{OBD}+\angle\text{BOD}+\angle\text{ODB}=180^\circ$
$\angle\text{BOD}=180^\circ-\angle\text{AOD}=180^\circ-70^\circ=110^\circ$
So $\angle\text{OBD}=180^\circ-\angle\text{BOD}-\angle\text{ODB}$
$=180^\circ-110^\circ-20^\circ$
$=50^\circ$
Now $\angle\text{ECD}=\angle\text{AOD}=70^\circ\ ($Corresponding angles$)$
In $\triangle\text{OBD}$
$\angle\text{OBD}+\angle\text{BOD}+\angle\text{ODB}=180^\circ$
$\angle\text{BOD}=180^\circ-\angle\text{AOD}=180^\circ-70^\circ=110^\circ$
So $\angle\text{OBD}=180^\circ-\angle\text{BOD}-\angle\text{ODB}$
$=180^\circ-110^\circ-20^\circ$
$=50^\circ$
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