MCQ
If $\text{ABC}$ and $\text{DEF}$ are similar triangles such that $\angle\text{A}=47^\circ$ and $\angle\text{E}=83^\circ,$ then $\angle\text{C}=$
- ✓$50^\circ$
- B$60^\circ$
- C$70^\circ$
- D$80^\circ$
✓
Answer
Correct option: A.
$50^\circ$
We have,
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\angle\text{A}=\angle\text{D}=47^\circ,\ \angle\text{B}=\angle\text{E}=83^\circ$ and $\angle\text{C}=\angle\text{F}=?$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ ($angle sum property$)$
$\Rightarrow47^\circ+83^\circ+\angle\text{C}=180^\circ$
$\Rightarrow130^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-130^\circ$
$\Rightarrow\angle\text{C}=50^\circ$
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\angle\text{A}=\angle\text{D}=47^\circ,\ \angle\text{B}=\angle\text{E}=83^\circ$ and $\angle\text{C}=\angle\text{F}=?$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ ($angle sum property$)$
$\Rightarrow47^\circ+83^\circ+\angle\text{C}=180^\circ$
$\Rightarrow130^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-130^\circ$
$\Rightarrow\angle\text{C}=50^\circ$
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