MCQ
In the given figures the measures of $\angle\text{D}$ and$\angle\text{F}$ are respectively
- A$30^\circ,20^\circ$
- B$40^\circ,50^\circ$
- C$50^\circ,40^\circ$
- ✓$20^\circ,30^\circ$
✓
Answer
Correct option: D.
$20^\circ,30^\circ$
In $\triangle\text{ABC},\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{A}+30^\circ+20^\circ=180^\circ$
$\Rightarrow \text{A}=130^\circ$
Again in,$\triangle\text{ABC} $ and $\triangle\text{DEF},$
$\frac{\text{AB}}{\text{AC}}=\frac{\text{EF}}{\text{ED}}$
$\angle\text{A}=\angle\text{E}=130^\circ$
$\triangle\text{ABC}\sim\triangle\text{EFD}\ ($Similarity$)$
$\therefore\angle\text{F}=\angle\text{B}=30^\circ$
$\therefore\angle\text{D}=\angle\text{C}=20^\circ$
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