MCQ
Mark $(\checkmark)$ against the correct answer.In the given figure, $\angle\text{A}=50^\circ,\text{CE}{\parallel}\text{BA}$ and $\angle\text{ECD}=60^\circ.$ Then, $\angle\text{ACB}={}?$
- A$50^\circ$
- B$60^\circ$
- ✓$70^\circ$
- D$80^\circ$
✓
Answer
Correct option: C.
$70^\circ$
In the figure,
Side $BC$ of $\triangle\text{ABC}$ is produced to $D$
$CE||BA$ is drawn
$\angle\text{A}=50^\circ$ and $\angle\text{ECD}=60^\circ$
$\text{AB}||\text{CE}$
$\angle\text{ABC}=\angle\text{ECD}$ (corresponding angle)$=60^\circ$
But in $\triangle\text{ABC,}$
$\angle\text{A}+\angle\text{B }+\angle\text{ACB }=180^\circ$ (Angles of triangles)
$\Rightarrow50^\circ+60^\circ+\angle\text{ACB}=180^\circ$
$\Rightarrow\angle\text{ACB}=180^\circ-50^\circ-60^\circ=70^\circ$
Side $BC$ of $\triangle\text{ABC}$ is produced to $D$
$CE||BA$ is drawn
$\angle\text{A}=50^\circ$ and $\angle\text{ECD}=60^\circ$
$\text{AB}||\text{CE}$
$\angle\text{ABC}=\angle\text{ECD}$ (corresponding angle)$=60^\circ$
But in $\triangle\text{ABC,}$
$\angle\text{A}+\angle\text{B }+\angle\text{ACB }=180^\circ$ (Angles of triangles)
$\Rightarrow50^\circ+60^\circ+\angle\text{ACB}=180^\circ$
$\Rightarrow\angle\text{ACB}=180^\circ-50^\circ-60^\circ=70^\circ$
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