Question
If ABC and DEF are similar triangles such that $\angle\text{A}=57^\circ$ and $\angle\text{E}=73^\circ,$ what is the measure of $\angle\text{C}?$
✓
Answer
We have,
$\triangle\text{ABC}\sim\triangle\text{DEF}$
we know that corresponding angle of similar triangle are equal.
$\angle\text{A}=\angle\text{D}=57^\circ$ and $\angle\text{B}=\angle\text{E}=73^\circ$
$\angle\text{C}=\angle\text{F}=?$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ (Angle sum property)
$\Rightarrow57^\circ+73^\circ+\angle\text{C}=180^\circ$
$\Rightarrow130^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-130^\circ$
$\Rightarrow\angle\text{C}=50^\circ$
Thus, $\angle\text{C}=50^\circ$
$\triangle\text{ABC}\sim\triangle\text{DEF}$
we know that corresponding angle of similar triangle are equal.
$\angle\text{A}=\angle\text{D}=57^\circ$ and $\angle\text{B}=\angle\text{E}=73^\circ$
$\angle\text{C}=\angle\text{F}=?$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ (Angle sum property)
$\Rightarrow57^\circ+73^\circ+\angle\text{C}=180^\circ$
$\Rightarrow130^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-130^\circ$
$\Rightarrow\angle\text{C}=50^\circ$
Thus, $\angle\text{C}=50^\circ$
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